fybsc Journal Sem I Final.docx

R. D. & S. H. NATIONAL COLLEGE & S. W. A. SCIENCE COLLEGE
BANDRA (W), MUMBAI 400050
F. Y. B. Sc. Journal SEMESTER-I
1
Skill 1: Vernier Callipers, Screw Gauge, Travelling
Microscope
Micrometer Screw Gauge:
The least count (L.C.) of the micrometer screw gauge is defined as
L.C. =
N
P
scale
circular
the
on
divisions
of
no.
Total
screw
the
of
Pitch

Where pitch of the screw = P = distance covered by the screw on the main scale (M.S.) in one rotation
of the circular scale (C.S.)
If P is in mm, the L.C. is in mm. If P is in cm, the L.C. is in cm.
Procedure for determining L.C. :
The main scale (M.S.) is marked in mm.
Count the total no. of divisions in 10 mm. Hence find the value of each main scale divisions (M) in
mm.
Example :
If there are 10 divisions in 10mm, then value of each main scale division
= M =
10
10
mm = 1mm
If there are 20 divisions in 10mm then value of each main scale division =
20
10
mm = 0.5mm.
To find the pitch of the screw (P) :
Rotate the circular scale (C.S.) through two or any even no. of complete rotations r in increasing order
of circular scale divisions. Note the divisions (n) moved on the M.S.
 Distance covered by the screw on the Main scale = X = n mm.
 Pitch of the screw P =
r
x
mm.
Total number of the divisions on C.S. = N
Determine the L.C. =
N
P
mm
Procedure for determine the zero error (Z) :
When the zero at the M.S. does not coincide with the zero of the C.S. when the two jaws are in
contact, there is a zero error. It can be positive or negative.

2
Positive zero error :
If the zero error is positive, as is shown in the diagram, directly read the C.S. reading (C.S.R.) which
coincides with the M.S. reference line.
 Zero error = Z = C.S.R. x L.C.
Negative zero error :
If the zero error is negative, as shown in the diagram. The C.S. reading (C.S.R.) which coincide with
the M.S. reference line is to be subtracted from N.
(the total no. of divisions on C.S.) This is then multiplied by the L.C. and denoted by a negative sign.
i.e. Z = N – (C.S.R. X L.C.)
Example :
If N = 100 & C.S. = 95 div, the Z = - (100 – 95) X L.C.
 Z = -10 X 0.001 cm = - 0.01 cm.

3
Total reading (TR) :
TR = M.S.R. + (C.S.R. X L.C.)
Where M.S.R. = Main Scale Reading
C.S.R. = Circular Scale Reading coinciding with Main Scale
L.C. = Least Count
Z = Zero error = C.S.R X L.C. for positive error and is to be subtracted
= - (C.S.R.) X L.C. for negative error and is to added.
Corrected Reading = T.R  Z
Linear Vernier Scale Instruments:
Least Count of Vernier Callipers =
divisions
scale
Vernier
of
Number
division
scale
main
smallest
of
Value
Note:
n divisions on Vernier scale coincide with (n – 1) divisions on Main scale.
To determine the zero error (z)
When the zero of the vernier scale (V.S.) lies to the right of the zero of the main scale (M.S.) then the
error is called positive zero error (z). (fig. 1)
Note the divisions of V.S. which coincides with any division of the M.S. this multiplied by the L.C.
gives the positive zero error.
Fig. 1
When the zero of the V.S. lies to the left of the zero of the M.S., then the error is called negative zero
error(z). (Fig. 2)
Fig. 2

4
Note the division of the V.S. which coincide with any divisions of Main Scale. Subtract this reading
from N, where N is the total no. of divisions of the V.S. This multiplied by the L.C. with a negative sign
gives the negative zero error (z).
Z = - [(Total no. of divisions on V.S.) – (the divisions which coincides with any div. on M.S.)] X
L.C. in cm.
i.e. Z = -[N – V.S.D.] X L.C.
 Total Reading T.R. = M.S.R. + V.S.R. X L.C.  Z.
OR
L C of vernier =
Smallest division on main scale
Total number of divisions on vernier scale
Skill 1 – A: Use of Micrometer Screw Gauge
Aim: To use a micrometer screw gauge to determine the diameter of the given wire in case of η by
torsional oscillations and diameter of the wire of flat spiral spring in case of Y by using flat spiral
spring.

5
Least count of Micrometer Screw Gauge:
Number of rotations given to circular scale = r = ______________
Distance covered by the screw on the main scale for N rotations = x = _________ cm.
 Pitch =
r
x
= __________ cm
Number of divisions on circular scale = N = __________ div.
 L.C. =
N
pitch
= __________ cm.
Zero error división = Z = ___________ div, Zero error Reading (ZER) = Z x LC = _____________ cm
Diameter of the given wire in case of η by torsional oscillations:
M.S.R.
in mm.
M.S.R. in
cm (a)
C.S.D.
Div.
C.S.R. = C.S.D  L.C.
in cm (b)
T.R. = a + b
in cm (c)
Mean T.R.
cm
 Corrected diameter of the wire = Mean T.R.  ZER = __________ cm.
Result: Diameter of the wire = ___________ cm
Diameter of the wire of flat spiral spring in case of Y by using flat spiral spring:
M.S.R. in
mm.
M.S.R. in
cm (a)
C.S.D.
Div.
C.S.R. = C.S.D  L.C.
in cm (b)
T.R. = a + b
in cm (c)
Mean T.R. cm

6
 Corrected diameter of the wire = Mean T.R.  ZER = __________ cm.
Result: Diameter of the wire = ___________ cm
Date & signature of Practical Incharge:____________________________
Skill 1 – B: Use of Vernier Callipers
Aim: To use a vernier calliper to determine the diameter of the given disc in case of η by torsional
oscillations, inner and outer diameter of the flat spiral spring in case of Y by using flat spiral spring and
breadth of the rectangular bar in case of bifilar pendulum.
Least count of Vernier Callipers:
Smallest division of main scale = a = __________ cm
Total number of divisions on vernier scale = b = ___________.
 Least Count of Vernier Callipers = 
b
a
______________ cm.
Zero Error = Z = _________ div, ZER = Z x LC = ____________ cm
To determine the diameter of the given disc:

7
M.S.R.
(a) cm
V.S.D.
Div
V.S.R = V.S.D X L.C.
(b) cm
T.R. = a + b
(c) cm
Mean TR
Cm
 Corrected reading = Mean T.R  ZER = _____________ cm
Result: Diameter of the given disc = ___________ cm
To determine the inner diameter of the given spring:
M.S.R.
(a) cm
V.S.D.
Div
(b) cm
T.R. = a + b
(c) cm
Mean TR
Cm
Result: Inner diameter of the given spring = ___________ cm
To determine the outer diameter of the given spring:
M.S.R.
(a) cm
V.S.D.
Div
(b) cm
T.R. = a + b
(c) cm
Mean TR
Cm
Result: Outer diameter of the given spring = ___________ cm
To determine the breadth of the given rectangular bar:
M.S.R.
(a) cm
V.S.D.
Div
(b) cm
T.R. = a + b
(c) cm
Mean TR
Cm

8
Result: Breadth of the given rectangular bar = ___________ cm
Skill 1 – C: Use of Traveling Microscope
Aim: To use a traveling microscope to determine the diameter of bore of a given capillary tube in
case of the experiment of surface tension.
Least count of the travelling microscope:
 Least Count of Traveling Microscope =LC = 
b
a
______________ cm.
To determine the diameter of the bore in a capillary tube using a Traveling Microscope:
Microscope Reading
Diameter
d = a ~ b
‘a’ cm ‘b’ cm

9
Mean diameter = _____________cm
Results: Diameter of bore of a given capillary tube = ___________ cm
Skill 2: Plotting Graphs
Graphs are diagrams of the functions and relations usually we plot that express phenomena in the
physical world. Usually we plot experimental data on an X-Y graph.
Graphs serve the following purposes:
1. To show what has happened.
2. To show relationships between quantities.
3. To show distribution.
The independent variable is plotted along the X – axis (abscissa)
The dependent variable is plotted along the Y – axis (ordinate)
While drawing a graph:
1. Select the layout of the graph on the graph paper.
2. Draw origin, axes, scale, units and quadrants.
3. Scale is normally written for 1cm on the axis.
4. Plot points from the observation set.
5. Calculate the slope and intercept (if required)
Exercises
1. Plot the following points and determine the slope and the intercept of the resulting graph.
Use a suitable scale.
X cm - 6 - 4 - 2 0 4 8 12
Y cm 8 6 4 2 -2 - 6 - 10
MSR
(cm)
VSD
(div)
VSR= VSD
x LC (cm)
TR=MSR+
VSR(cm)
MSR
(cm)
VSD
(div)
VSR= VSD
x LC (cm)
TR=MSR+
VSR(cm)
(cm)

10
2. Plot the following points. Use a suitable scale.
X cm -4 -3 -2 -1 0 1 2 3
Y cm 9 4 1 0 1 4 9 16
3. Plot the following points. Use a suitable scale.
X sec 1 2 3 4 5 6
Y Volt 0 0.69 1.10 1.39 1.61 1.79
4. Plot the image distance (v) and the object distance (u). Determine the focal length (f) using the
formula, 𝑓 =
𝑢𝑣
𝑢+𝑣
u cm 15.0 17.5 20.0 23.0 27.0 30.0 35.0 40.0 45.0 50.0 60.0
v cm 75 44 33.3 27.5 23.3 21.5 19.5 18.2 17.3 16.7 15.8
5. Plot the graph of power delivered versus load resistance and determine the load resistance
where the power delivered is maximum.
RL Ω 10 20 30 40 50 60 70 80 90 100 150 200
PL mW 0 24.6 40 49.6 55.6 59.6 61.2 62.2 61.6 61.6 56.7 51.0

11
Skill 3: Spectrometer – Schuster’s Method
T – Telescope P – Prism Table C – Collimator
E – Eye-piece Fp – Fixing screw L – Lens
O – Objective Tp – Tangent screw FC – Focusing screw
Ft – Focusing screw SP – Screw for fixing table S - Slit
to verniers
Lt – Levelling screw LP – Levelling screw LC – Levelling screw
St – Fixing screw S1, S2, S3 – Levelling screw FS – Screw for Adjusting
Tt – Tangent screw for slow motion of the instrument slit width
RAY DIAGRAM
PROCEDURE:
1. Leveling the Prism Table (P.T.) :
To the base of the prism table are attached three screws which form the equilateral triangle.
To level the Prism table set the spirit level along the line joining any two screws say (a) and
(b). Adjust either of the screws as required and the bubble in the centre. Set the spirit level
perpendicular to the line joining (a) and (b) and adjust the third screw so as to bring the

12
bubble in the centre. If the bubble remains in the centre in the both these position of the spirit
level, then the P.T. is leveled.
2. Adjustment for parallel light – Schuster’s method
1. Rotate the prism table slowly and follow the refracted image of slit with the naked
eye. (If the source is a multi-chromatic a number of lines will be seen. In such a case
take one line preferably yellow line as the reference line). The image of the slit begins
to move towards the collimator. At a certain stage it will be observed that the image
stops and recedes (or goes back). Adjust the telescope to see the image of slit in this
position and clamp it. Rotate the prism table slowly to see the exact position at which
the image turns back and the clamp the prism table again. Now adjust the position of
telescope with the fine motion screw in such a way that the intersecting point of cross
wires coincides with the image of the slit.
2. Adjust focusing screw of collimator or the telescope till image of spectrum is sharp
and focused.
3. Starting from minimum deviation position, prism table is turned so that the refracting
edge A turns towards telescope.
4. The image now appears defocused. Adjust the focusing screw of telescope till image
of spectrum is sharpest.
5. Keep telescope fixed in this position. Now turn prism table so that the refracting edge
a turns towards collimator.
6. The spectrum appears defocused. Adjust focusing screw of collimator to get a sharp
image.
7. Repeat the steps alternatively till image appears equally well focused for both the
positions of the prism table. Now spectrometer is focused for parallel light.
Least Count of Spectrometer:
Smallest division of main scale = a = __________
Total number of divisions on vernier scale = b = ___________
 Least Count of Spectrometer =LC = 
b
a
______________

13
Skill 4: Use of Digital Multimeter
Diagram :
1. Measurement of Resistance
Keep the range selector on resistance range.
Keep black wire on common socket.
Keep red wire on resistance position i.e., .
Take a suitable resistance. Connect it across DMM. Note the resistance on the screen.

14
If 1 appears on the screen, this indicates over range.
Select now a suitable range so that accurate measurement of resistance can be recorded.
Observations:
Measurement of Resistance
Colors Calculated
Resistance 
Measured
Resistance 
Range selected
Band 1 Band 2 Multiplier
Band 3
Tolerance
2. Measurement of DC voltage
Keep the range selector on "DC Volt" range
Keep black wire of DMM in common socket and red wire in the socket marked (V,).
Connect the DMM across the dc source. Starting with the highest dc voltage range, select a
suitable range and note down the dc voltage.
Repeat for two more unknown voltages.
Observations:
Measurement of dc Voltage
3. Measurement of DC Current
Adjust dc source to 1V. Connect a series resistance of 1 k.
Unknown Voltage Range Selected Measured Value
(V)
V1
V2
V3

15
Keep the range selector on “DC mA” range.
Keep red wire in DC mA Socket and the black wire in common socket.
Now connect this DMM in series. Starting with the highest current range, select a suitable
range and note down the dc current.
Now change the source voltage to 5V and 10V and measure the current again in each case.
Observations:
Measurement of Current
Voltage selected
(V)
Range Selected Measured Value
(mA)
1
5
10
4. Measurement of ac (R.M.S. Value)
Keep the range selector on “ac volts”.
Plug the black wire in common socket and the red wire in socket marked (V,).
Connect the DMM across ac signal generator. Starting with the highest ac voltage range,
select a suitable range and note down the ac voltage.
Note that it is the rms value of ac voltage.
Repeat for two more unknown voltages.
Observations:
Measurement of ac Voltage
Unknown Voltage Range Selected Measured Value
(V)
V1
V2
V3

16
1: η of a wire by Torsional Oscillations
Aim : To determine the modulus of rigidity () of a wire by torsional oscillations.
Apparatus : A thick heavy disc with nut and chuck arrangement to clamp the wire, vernier
calipers, micrometer screw gauge, long and thin wire, stop watch, meter
scale, weight box, balance.
Diagram:
Formula : 1. I =
2
MR2
where, I = M.I. of the disc,
M = mass of the disc,
R = Radius of the disc
2.  =
4
r
8
. I.
2
T
l
where, l = length of the wire
r = radius of the wire
T = period of oscillations
Procedure :
1. Weigh the disc on a digital balance.
2. Measure the diameter of the disc with vernier calipers. Take at least 4 readings.
3. Suspend the disc by the wire. Measure the diameter of the wire with a micrometer screw
gauge. Take at least ten readings along the entire length of the wire.
4. For the length l of the wire, set the disc into torsional oscillations. Find the time for 20
oscillations. Hence determine the period of oscillations.
5. Repeat the procedure for at least six different lengths. Each time change the length by about
10 cms.
6. Plot a graph of l against T2.

17
Observations :
1. Mass of the disc = M = _______________ gm
2. Least count of Vernier Callipers
b
a
______________ cm.
Zero Error = Z = _________ div = ____________ cm
Diameter of disc: (2R)
M.S.R.
(a) cm
V.S.D.
Div
(b) cm
T.R. = a + b
(c) cm
Mean TR (2R) cm
 Radius of the disc = R = _________cm.
3. Least Count of Micrometer screw gauge.
L.C. =
divisions
circular
of
no
total
pitch
Value of smallest division on Main Scale = _________ mm = __________ cm
Pitch =
10
rotations
10
in
Scale
Main
on
covered
ce
tan
dis
= _____cm
 L.C. = _________ cm.
Zero error micrometer screw gauge =Z =________ div. ZER = Z x LC = ____________ cm
Diameter of wire (2r)
M.S.R.
in mm.
M.S.R. in
cm (a)
C.S.D.
Div.
C.S.R. = C.S.D  L.C.
in cm (b)
T.R. = a + b
in cm (c)
Mean T.R.
(2r) cm

18
 Mean diameter of the wire = 2r = ________ cm.
 Mean corrected diameter of the wire = 2 r  ZER = ________ cm
 Radius of the wire = r = __________ cm.
Observations for Period of Oscillations:
length of the
wire l cm.
Time for 20
oscillation
Period T = (t/20) sec T2
(sec)2 2
T
 cm/sec2
t1
sec
t2
sec
Mean
t sec
40
50
60
70
80
90
100
Graph:
Calculations:
1. M.I. of disc = I = ½ MR2 = _________ g – cm2
2.  = 4
r
8 

x slope = ____________  ____________ = ___________ dyne/cm2
Results:
1. M.I. of disc = I = ___________gm cm2.
2.  = ________________________ dyne/cm2.
Slope = _______ cm/sec2
(0,0)
T 2
l

19
Question Slip
F. Y. B. Sc. SEMESTER-I
PHYSICS PRACTICAL EXAMINATION
GROUP – A: η BY TORSIONAL OSCILLATIONS
Marks
Allotted
1 Measure the diameter of the wire using a micrometer screw
gauge. Take at four readings. Hence obtain the mean radius
(r = d /2) of the wire.
06
2 Now suspend the disc by a long thin uniform wire of length 𝑙= 40
cm, from a rigid support. Rotate the disc through a small angle in
the horizontal plane and release it so that it performs torsional
oscillations. Find the time (t) for 10 oscillations.
04
3 Calculate the period of oscillaton T, where, T = t 10 .
⁄
Also calculate 𝑙 T2
⁄ .
03
4 Repeat steps 2 and 3 for three more different values of lengths l
(50, 60 & 70) cm. Find mean l/T2
.
21
5 Determine the modulus of rigidity η of the wire using the
relation: η = 2
4
8π
T
l
r
Ι
 .
Moment of inertia of the disc I = _________ gm cm2
06
Total 40

20
2: Angle of Prism
Aim : To determine the refracting angle of a prism
Apparatus : Spectrometer, prism, spirit level, source of light, magnifying lens.
Ray Diagram :
Procedure:
1. Placing the prism on the prism table :
The prism table has concentric rings on it, the prism is kept on the table such that the three
vertices of the triangular prism are symmetrically placed w.r.t. the concentric rings and the
ground surface of the prism is perpendicular to the collimator.
2. Leveling the Prism Table (P.T.) using spirit level:
To the base of the prism table are attached three screws which form the equilateral triangle.
To level the Prism table set the spirit level along the line joining any two screws say (a) and
(b). Adjust either of the screws as required and get the bubble in the centre. Next set the
spirit level perpendicular to the line joining (a) and (b) and adjust the third screw so as to bring
the bubble in the centre. If the bubble remains in the centre in the both these position of the
spirit level, then the P.T. is leveled.

21
2. Optical Leveling of the prism table and finding the refracting angle of the prism:
1. Position the prism table so that the refracting edge ‘A’ faces the collimator, the
resultant collimating beam being reflected by faces AB and AC respectively.
2. The slit is then viewed with the telescope by reflecting in face AB. By means of
leveling screws X and Y, the image is centered in the field of screw.
3. The telescope is then swung round to receive light reflected by face AC, and by
means of Z alone, the slit image is again centered.
4. It is desired to return to the first setting to check that the adjustment has not been
disturbed during the second setting. This is because face AB may not be exactly
perpendicular to XY.
5. If the slit is not in the centre of view from both the surface AB and AC, then repeat
steps 2 and 3 alternatively so that the image of the slit is in the centre of field of view
when seen from both the sides of the prism.
6. Now coincide the image of the slit as seen from AB, exactly with the vertical cross-
wire of the eye-piece. Note the corresponding window readings
(window 1 and window 2).
7. Repeat 6, viewing the image of the slit from AC.
Observations:
Least Count of Spectrometer:
b
a
______________
Window
Spectrometer Reading
0
= a
~ b
Mean

Angle of
prism
A =
(/2)0
Face AB (a)0
Face AC (b)0
MSR VSD VSR TR MSR VSD VSR TR
Window 1
Window 2
Result:
The angle of prism = A = _______________0.

22
Question Slip
GROUP – B: ANGLE OF PRISM
Marks
Allotted
1 Draw the ray diagram for determining the angle of prism. 05
2 Align the collimator axis with the axis of the telescope. 03
3 Adjust the spectrometer for parallel light using distant object. 05
4 Optically level the prism table. 05
5 Place the prism at the centre of the prism table with its
refracting edge facing the collimator lens. Adjust the telescope
to obtain the image of the slit reflected from one face of the
prism, in line with the cross-wires. Record the two window
readings.
08
6 Adjust the telescope to obtain the image of the slit reflected
from the other face of the prism, in line with the cross-wires.
Record the two window readings.
08
7 Determine the mean refracting angle of the
prism.
06
Total 40

23
3: Refractive Index of Material of Prism
Aim : To determine the refractive index of material of prism.
Apparatus : Spectrometer, prism, spirit level, source of light, magnifying lens.
Ray Diagram :
Procedure :
1. Adjust the spectrometer for parallel light (Schuster’s method)
2. Keep the prism at the centre of the prism table so that the ground face BC is approximately
parallel to the collimator, and parallel light from collimator is incident on the refractive surface
AC and emerges from the other refracting surface AB.
3. Mount prism on prism table with one of its refracting faces (AB or AC) perpendicular to the
axis of the collimator. Now rotate the prism table gradually such that refracting edge A moves
away from the collimator. View the spectrum from the other refracting face. The spectrum
shifts in a particular direction then stops and shifts back in opposite direction. The location of
the prism at which the spectrum stops or changes direction is called minimum deviation
position. Adjust telescope so as to observe this spectrum in the minimum deviation position.
4. Remove the prism and turn the telescope to be in the line with the collimator so that the point
of intersection of cross-wires coincides with the image of slit seen directly. Note the
corresponding spectrometer readings on windows X and Y for this position T2 of telescope.
This is called direct reading.

24
Observation:
Least Count of Spectrometer
b
a
______________
1. Angle of prism A: ____________.
2. To determine the angle of minimum deviation (m).
Line
used
Yellow
Window
Spectrometer Reading
m =
a ~ b
Mean
m
m position ‘a’ Direct reading ‘b’
MSR VSD VSR TR MSR VSD VSR TR
X
Y
Calculations:
To determine the refractive index of the material of the prism:
 =
2
sin
2
sin
A
A m





  
= _____________.
Results:
1. The angle of minimum deviation = m = __________
2. The refractive index of prism =  = ___________

25
Question Slip
GROUP – B: R.I. of MATERIAL of PRISM
Marks
Allotted
1 Draw the ray diagram for determining the refractive index of
the material of prism.
04
2 Align the collimator axis with the axis of the telescope. 03
3 Adjust the spectrometer for parallel light using distant object. 03
4 Optically level the prism table. 05
5 Keep the prism at the centre of the prism table with its base
parallel to the incident light. Observe the spectrum.
04
6 Adjust the minimum deviation position. Record the two
window readings for green spectral line at this position.
Remove the prism and take the direct reading.
14
7 Find 𝛿𝑚, the angle of minimum deviation for green spectral
line.
04
8 Calculate the refractive index for the green spectral line.
µ =
 
 
2
/
sin
2
sin
A
δ
+
A m
Given: Angle of the prism A = 600
03
Total 40

26
4: Combination of Lenses
Aim : To determine the focal length of the lens system by the method of
magnification.
Apparatus : Lens system, scale, lamp, screen, Index pin.
Diagram :
Formula :
1.
2
1
2
1 f
f
d
f
1
f
1
F
1



where, f1 is the focal length of the first lens, f2 is the focal length of the second lens;
F is the focal length of the lens system, d is the distance between the two lenses.
2. m =
u
v
where, m is the magnification produced by a lens system; v is the image distance; u is
the object distance.
Also, m = I/O where I is the size of the image; O is the size of the object.
Procedure:
1. Arrange the lens system so that the distance between the two lenses is d cm.
2. Illuminate the object using a lamp. Place the object on one side of the lens system and
screen on the other side.

27
3. Keep the object at a suitable distance from lens and adjust the position of the screen so that a
distinct real magnified image is obtained on the screen.
4. Measure the size of the image. Measure the distance between the object and lens near the
object (u). Measure the distance between the screen and lens near the screen (v)
5. Repeat the procedure for various object distances, such that the size of the image changes
appreciably. (f1 & f2).
6. Also find the individual focal lengths of the lenses, by auto collimation method.
Observation:
1. size of the object = O = ________cm.
2. Distance between the two lens = d = _______ cm.
Object
distance ‘u’
cm
Image
distance ‘v’
cm
size of Image
‘I’ cm
Magnification
m = I/O
1 + m 1 + 1/m
By auto collimation method, f1 = ______ cm, f2 = _________ cm.
Graphs:
Calculations:
1. From the graph of u v/s 1 +
m
1

28
Intercept a = ____________ cm.
Slope = F = ____________ cm.
2. From the graph of v v/s 1 + m.
Intercept = b = __________ cm
Slope = F = __________ cm.
3. F by calculation:
2
1
2
1 f
f
d
f
1
f
1
F
1


 = ________
1
cm
(where f1 & f2 are found by auto collimation method)
 F = ___________ cm.
Results:
1. F from the plot of the u vs 1 +
m
1
is = ____________ cm.
2. F from the plot of vs 1 + m is m = ____________ cm.
3. F calculation = ___________ cm.
4. a = _____________cm b = _______________ cm.

29
Question Slip
GROUP – B: COMBINATION of LENSES
Marks
Allotted
You are given two lenses, a lamp, an object and a screen.
1 Arrange the apparatus to determine the focal length of a
combination of two lenses separated by a fixed distance‘d’.
04
2 Keep the object of size O = 1 cm at a suitable distance from
the lens nearer to it and adjust the position of the screen so
that a distinct, real, magnified image is obtained. Note the
image size ‘I’ and the distance of the image ‘v’ from the lens
nearer to the screen. Determine the magnification m = I/O.
10
3 Repeat the experiment for three more different values of ‘u’
and ‘v’. Calculate the magnification in each case, m = I/O.
09
4 Find the individual focal lengths of the lenses (i.e. f1 and f2)
using a distant object.
04
5 Plot a graph of v (y- axis) versus 1 + m (x- axis). Hence
determine b and f.
10
6 Calculate ‘f’ using the relation
2
1
2
1 f
f
d
f
1
+
f
1
=
f
1
 and compare with the value
obtained in step 5.
03
Total 40

30
5: J by Electrical Method
Aim: To find the mechanical equivalent of heat produced by the consumption of electrical
energy.
Apparatus: 15V dc source of 2 Amperes, calorimeter with stirrer, coil, 20V DC digital voltmeter,
2A digital ammeter, stop-watch, connecting wires.
Circuit Diagram:
Formula:
  
1
2
w MS
mS
VIt
H
W
J









Where, J is the mechanical equivalent of heat or Joules constant;
W is the work done in Joules, i.e. the electrical energy supplied to the coil;
H is the heat produced in calories;
V is the potential difference applied in Volt;
I is the current in Amperes;
t is the total time for which the current was passed
M is the mass of the empty calorimeter with stirrer;
M
M
m /

 is the mass of water in calorimeter;
/
M is the mass of calorimeter + stirrer + water;

31
SW is the specific heat of water;
S is the specific heat of the calorimeter;
1
2 

 is the rise in the temperature of water and

 is the fall in temperature due to radiation.
Procedure:
1. Weigh the calorimeter along with the stirrer and find its mass M.
2. Fill the calorimeter (about 2/3rd of its volume) by water. Weigh it along with the stirrer and find
its mass
/
M . Hence, find the mass of the water taken ‘m’.
3. Introduce the coil into the calorimeter so that it is well immersed in the water. Insert the
thermometer in the calorimeter so that its bulb is close to the coil but is not in contact with the
coil.
4. Connect the circuit as shown in the diagram.
5. Switch on the supply and adjust it to get a current of 1 A. Switch off the supply.
6. Note the initial temperature 1 of water. Now switch on the supply and simultaneously start
the stop watch.
7. Note down the temperature of water at regular intervals of time. Stir the water continuously.
8. Note the readings of the current I and the voltage V at regular intervals of time (3 readings)
9. When the temperature of water has risen by 10 degrees above 1, note 2. Switch off the
supply.
10. Note the total time t for which the current was passed.
11. Plot a graph of  (in degrees) (y-axis) versus time (in seconds) (x-axis).
12. From the graph determine the radiation correction . Hence calculate J using the formula.
Observations:
1. Mass of empty calorimeter + stirrer = M = ___________ g
2. Mass of calorimeter + stirrer + water =
/
M = __________ g
3. Mass of water in the calorimeter = M
M
m /

 = ___________ g
4. Specific heat of water SW = 1 cal / g / C
5. Specific heat of calorimeter + stirrer = S = 0.1 cal / g / C
6. Initial temperature of water 1 = _________ C

32
7. Final temperature of water after heating 2 = _________ C
8. Time for which current was passed = t = _________ sec
9. Current passing through the coil I
(a) ________ A (b) __________ A (c) _________ A
 Mean current I = _________ A
10. P.D across the coil V
(a) ________ V (b) _________ V (c) ________ V
 Mean voltage V = _________ volt
Time t sec Temperature
 C
 C
 C
0 210 420
30 240 450
60 270 480
90 300 510
120 330 540
150 360 570
180 390 600
Graph:
Calculations:
From the plot of  versus t,  = __________ C

33
  
1
2
W MS
mS
VIT
J








 = ___________ J / cal
Results:
Radiation correction  = _____________ C; J = ___________ J / cal
Question Slip
GROUP – A: J by ELECTRICAL METHOD
Marks
Allotted
You are given a resistance R in the form of a coil immersed in
a calorimeter of mass M, specific heat S = 0.1 cal / g/ C,
containing m grams of water of specific heat Sw =1 cal / g /
C.
1 Draw the required circuit diagram. 04
2 Make the connections after getting the circuit checked. Do not
switch on the current until you have obtained the examiner’s
permission to do so.
04
3 Note the initial temperature 1 of water. Switch on the supply
and adjust it to get a current of 1 A. Start the stop watch.
02
4 Stir the water continuously and note down the temperature of
water at regular intervals of time till the temperature of water
rises 100
above 1.
10
5 Note the total time for which the current was passed, when the
temperature of water has risen by 100
above 1. Note 2.
Switch off the supply.
04
6 Note the readings of the current I and the voltage V at regular
intervals of time (3 readings)
04

34
7 Plot a graph of  (in degrees) (y-axis) versus time (in
seconds) (x-axis).
06
8 From the graph determine the radiation correction . Hence
calculate J using the formula:
  
1
2 

 





MS
mS
VIt
H
W
J
w
06
Total 40
6: BIFILAR PENDULUM
Aim: To determine the moment of inertia of the given bar about the vertical axis passing
through the midpoint of the bar by bifilar pendulum method. Compare it with
the moment of inertia of the bar found by direct measurement and formula.
Apparatus: The given bar with a series of hooks fitted along its length, stand with the suspension
arrangement, string, stop-watch, meter scale, balance, vernier calipers, etc.
Diagram:
Formulae: Moment of Inertia for rectangular bar (by experiment) I =
mgd1d2T2
16π2L
Moment of Inertia for rectangular bar (by graph) I =
mgd1d2
16π2
× (slope of T2
against L)
Moment of Inertia for rectangular bar (by calculations) I = m [
l2+b2
12
]
Procedure:
1. Find the mass (m) of the given bar by weighing it on a balance correct up to one gm.

35
2. Select two hooks lying symmetrically near the two ends of the bar. Take two strings having the
same length (L). Tie the lower ends with these hooks and suspend the bar from the other ends
from the stand as shown in the diagram. Since the strings have the same length the bar
becomes horizontal. Measure the length of the string (L) using the meter scale.
3. Measure the distance (d1) between the upper ends of the string and the distance (d2) between
the lower ends of the string using a meter scale. Select the hooks so that (d2) is nearly equal to
(d1). We have to keep the distances constant throughout the experiment. Now the bifilar
pendulum is ready.
4. Give a small angular displacement to the bar in the horizontal plane. The bar is set into the
torsional oscillations in the horizontal plane about the vertical axis, passing through the midpoint
of the bar. See that the amplitude of the oscillations is small.
5. Find the time for 20 oscillations of the bar. Take the readings two times and find the average
time. From this calculate the period (T) of the oscillations of the pendulum.
6. Calculate the moment of inertia (I) of the bar using the formula,
7. In this manner, take 7 readings by changing the length (L) of the pendulum. But keep the
distance (d1) and (d2) constant throughout the experiment. Find the mean value of the moment
of inertia (I) of the bar.
8. Plot a graph of T2 against L and find the slope. Hence calculate moment of inertia (I) from
graph.
9. For rectangular bar, you can find the moment of inertia by direct measurement using the
corresponding formula. You have already found out the mass (m) in the original experiment.
The length (l) of the bar can be measured using a meter scale. The breadth (b) of the
rectangular bar can be found out using a vernier calipers. Hence the moment of inertia (I) of any
bar can be calculated.
10. Compare the value of the moment of inertia of the bar found in the experiment and that found
by direct measurement and the graph.
Observations:
Mass of the given bar = m = _________gm.
Distance between the upper ends of the string = d1 = __________ cm
Distance between the lower ends of the strings = d2 = _________ cm
Obs.
No.
Length of
each string
L (cm)
Time for 20 oscillations Period of
oscillations
T = t 20
⁄
sec
Moment of inertia of
bar I =
mgd1d2T2
16π2L
gm. cm2
t1 sec t2 sec Mean t sec

36
Mean (I) = ____ gm. cm2
Determination of the moment of inertia by measurement
For Rectangular bar
Mass of the bar = m= _____gm.
Length of the bar = 𝑙 = ______ cm.
Least count of Vernier calipers = _______ cm.
Readings for the breadth of the bar:
MSR cm VSD VSR = VSD x LC
cm
TR = MSR + VSR
(b) cm
Mean breadth
of the bar
b =
_________cm
Calculations:
Moment of Inertia for rectangular bar I = m [
l2+b2
12
]= ___________ gm cm2
Graph:

37
Calculations:
Moment of Inertia for rectangular bar (by graph) I =
mgd1d2
16π2
× (slope of T2
against L)
= ___________ gm cm2
Results:
Moment of inertia of the given bar:
By experiment, I = _____ gm cm2
By graph, I = ________ gm cm2
By measurement and formula, I = __________ gm cm2

38
Question Slip
GROUP – A: BIFILAR PENDULUM
Marks
Allotted
1 Find the mass (m) of the given rectangular bar using a digital
balance.
02
2 Measure the length (l) using meter scale and breadth (b) at 3
different points of the rectangular bar using vernier callipers
respectively. Find the mean breadth (b).
03
3 Calculate the moment of inertia of the bar using the formula: I =
m(𝑙2+b2)
12
02
4 Select two hooks lying symmetrically near two ends of the bar.
Take two strings having the same length (L=30cms). Tie the lower
ends with these hooks and suspend the bar from the other ends
from the stand. Since the strings have the same length, the bar
02

39
becomes horizontal.
5 Measure the distance (d1) between the upper ends of the string and
distance (d2) between lower ends of the string. (d1≈ d2). This
distance d1 and d2 must remain the same throughout the
experiment.
02
6 Give a small angular displacement to the bar in the horizontal
plane. Set the bar into torsional oscillations in the horizontal plane
about vertical axis, passing through the midpoint of the bar. The
amplitude of oscillations must be small.
Measure the time for 20 oscillations, take two trials and find the
average time (t). Hence calculate the period T (T= t /20) of the bar.
04
7 Repeat steps 3 to 6 for four more values of L (i.e. 40, 45, 50,
55cms).
16
8 Draw a graph of T2
(y-axis) vs L (x-axis) and find the slope of the
plot.
04
9 Determine the moment of inertia of the bar using the relation:
I =
mgd1d2T2
16π2L
=
mgd1d2
16π2
× (slope of T2
vs L)where, g = 980 cm /s2
04
10 Compare the values of moment of inertia obtained in steps 3 and 9. 01
Total 40
7. Determination of Ү using Flat spiral spring
Aim: To determine the Young’s modulus (Y) of the material of the flat spiral spring.
Apparatus: Flat spiral spring, hanger with slotted weight, stop watch, telescope, vernier calipers,
micrometer screw gauge.
Formulae:
1. η=
16π2N(M+me)(R)
̅
̅
̅
̅3
(r)
̅̅̅̅4T1
2
where N = total number of turns in the spring; 𝑟 = mean radius of the wire of the spring;
𝑇1= period of oscillation in vertical direction, 𝑚𝑒= effective mass of the spring =
1
3
x (actual mass of the spring = m)
2. 𝜎 =
𝑌
2𝜂
− 1 , Hence, 𝑌 = 2𝜂(𝜎 + 1)
Where, η = modulus of rigidity, 𝑌 = Youngs Modulus, 𝜎 = Poisson’s ratio = 0.35
Procedure:
1. Count the total number of turns of the spring.
2. Weigh the spring and find its mass “m”.

40
3. Find inner diameter (D1) and the outer diameter of the screw (D2) using vernier calipers,
hence find mean radius 𝑅.
4. Using a micrometer screw find the diameter of the wire of the spring at (10) different places,
hence find the mean radius𝑟.
5. Clamp the spring at its upper end in a stand and suspend it vertically.
Oscillations in a vertical direction:
6. Suspend a hanger of mass (M) from the lower end of the spring. Load it with the maximum
mass. Fix a pin horizontally at the lower end. Focus a telescope on the pin and adjust it so
that horizontal cross wire coincides with pin.
7. Give a small displacement to hanger in the vertical (download) and release so that it starts
oscillating in vertical direction. Find out the time for 20 oscillation, take the reading twice. Find
period (T1) of the oscillation.
8. Remove one of the slotted mass from the hanger and repeat step (7).
9. Repeat step (8) for 4 more decreasing value of mass.
10. Plot a graph of M vs. T1
2and determine η. Also determine the value of the ‘M’ form the
intercept of the graph. Compare it with the mass of spring ‘M’
Observations:
Total number of turns in the spring =N= _________
Mass of the spring (m) =_________.gm
Least count of Vernier Callipers:
b
a
______________ cm.
To determine the inner diameter of the given spring:
M.S.R.
(a) cm
V.S.D.
Div
(b) cm
T.R. = a + b
(c) cm
Inner diameter of the
given spring D1 cm
To determine the outer diameter of the given spring:
M.S.R. V.S.D. V.S.R = V.S.D X L.C. T.R. = a + b Outer diameter of the

41
(a) cm Div (b) cm (c) cm given spring D2 cm
Sr.no Inner
diameter
D1
Cm
Outer
diameter
D2
Cm
Radius=
R=
𝐷1+𝐷2
4
Cm
1
2
3
4
5
Mean 𝑅=
Diameter of the wire of the spring (d):
Least count of Micrometer Screw Gauge:
Number of rotations given to circular scale = r = ______________
Distance covered by the screw on the main scale for N rotations = x = _________ cm.
 Pitch =
r
x
= __________ cm
Number of divisions on circular scale = N = __________ div.
 L.C. =
N
pitch
= __________ cm.
Zero error división = Z = ___________ div, Zero error Reading (ZER) = Z x LC = _____________ cm
M.S.R.
in mm.
M.S.R.
in cm
(a)
C.S.D.
Div.
C.S.R. =
C.S.D  L.C.
in cm (b)
T.R. = a + b
in cm (c)
C.R. = T.R.± ZER
in cm (d)
r=d/2
cm

42
Mean 𝒓
̅ = ____________cm
Reading of oscillation in vertical direction:
No Mass suspended
M(g)
Time for 20 oscillations Period 𝑇1=
t/20
Sec
T1
2
Sec 2
t1 sec t2 sec Mean t
sec
1
2
3
4
5
Graphs:
Calculations:
1. 𝜂 =
16π2N(M+me)R
̅3
r
4
T1
2

43
𝜂 = 16π2nR
3
r
4 × (slope of the graph T1
2 vs M)-1
𝜂 = ………..dyne/cm2
= ………….N/m2
2. 𝜎 =
𝑌
2𝜂
− 1, Hence, 𝑌 = 2𝜂(𝜎 + 1), where 𝜎 = Poisson’s ratio = 0.35
𝑌 = ………..dyne/cm2
= ………….N/m2
Results:
1. Modulus of rigidity of the material of the wire = 𝜂 =______________________.N/m2
2. Young’s modulus of the material of the wire =𝑌 =_______________________.N/m2
Question Slip
GROUP – A: Y by FLAT SPIRAL SPRING
Marks
Allotted
1 Using a micrometer screw measure the diameter of the wire of
the given spring at three different points and hence determine the
mean radius r of the wire.
06
2 Find inner diameter (D1) and the outer diameter of the screw (D2)
using vernier callipers at two different points, hence find mean
radius R of the spring.
04

44
3 Count the number of turns N of the spring. Find the mass M of
the spring.
02
4 Clamp the spring to a rigid support. Attach a mass M at its lower
end and set it oscillating vertically. Observe the oscillations
through a telescope and determine the periodic time T. Repeat the
procedure for three more values of M.
12
5 Plot M (y- axis) against T2
(x- axis) and Find the slope of the plot. 08
6 Determine the Modulus of rigidity η of the material using the
relation 𝜂 =
16π2N(M+me)𝑅3
𝑟4𝑇2
, where, me is the effective mass of the
spring.
∴ η =
16π2
N𝑅3
𝑟4
x (slope of the graph M vs T2
)
04
7 Hence calculate Y. Given: Y = 2η(σ + 1) and σ = 0.35 04
Total 40
8: THERMISTOR CHARACTERISTICS
Aim: To study the thermal characteristics of a given thermistor.
Apparatus: Thermistor, digital multimetr (DMM), hard glass tube, water bath, thermometer,
retort stand, connecting wires.
Circuit Diagram:

45
Formula: α =
1
R
dR
dT
Procedure:
1. Take water in container and place the container on stand and heat the water. Immerse
thermistor and thermometer placed in a test tube in the water bath. Connect a DMM in
the resistance measurement mode across the thermistor.
2. Draw the necessary diagram of the setup made.
3. Note the room temperature (𝜃) and measure the resistance (R) of the thermistor.
4. Increase the temperature of the water in a beaker in steps of 5°C (take six more readings).
5. Note down the temperature (𝜃) and corresponding resistance (R) of the thermistor with
the help of Ohm meter / DMM.
6. Plot a graph of temperature (𝜃) on X-axis and Resistance (R) on Y-axis. This graph shows the
characteristics of thermistor.
7. From the graph find the slope
𝑑𝑅
𝑑𝜃
at two temperatures 40°C and 60°C.
8. Calculate the temperature coefficient of resistance (𝛼) at 40°C and 60°C using the
relation: 𝛼1 =
1
𝑅1
(
𝑑𝑅
𝑑𝜃
)
𝜃1
Observations:
(1) Room Temperature: ____________℃
(2) Resistance of the thermistor at room temperature: ____________Ω
Observation Table:
Obs. No. Temperature 𝜃℃ Resistance of Thermistor R Ω

46
1 30/ RT
2 40
3 50
4 60
5 70
6 80
7 90
Graph:
Calculations:
1. α1 =
1
R1
(
dR
dT
)
θ1
= ____________
2. α2 =
1
R2
(
dR
dT
)
θ2
= ___________
Result:
1. The temperature coefficient of resistance: α1 = ____________℃ , α2 = ___________℃
2. The given thermistor has a negative temperature coefficient of resistance.
Question Slip

47
GROUP – B: THERMISTOR CHARACTERISTICS
Marks
Allotted
1 Take water in container and place the container on stand and heat
the water. Immerse thermistor and thermometer placed in a test
tube in the water bath. Connect a DMM in the resistance
measurement mode across the thermistor. Draw the necessary
diagram of the setup made.
04
2 Note the room temperature (𝜃) and measure the resistance (R) of
the thermistor.
03
3 Increase the temperature of the water in a beaker in steps of 5°C
(take six more readings). Note down the temperature (𝜃) and
corresponding resistance (R) of the thermistor with the help of
Ohm meter / DMM.
18
4 Plot a graph of temperature (𝜃) on X-axis and Resistance (R) on
Y-axis. This graph shows the characteristics of thermistor.
05
5 From the graph find the slope
𝑑𝑅
𝑑𝜃
at two temperatures 40°C and
60°C.
05
6 Calculate the temperature coefficient of resistance (𝛼) at 40°C and
60°C using the relation: 𝛼1 =
1
𝑅1
(
𝑑𝑅
𝑑𝜃
)
𝜃1
05
Total 40

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