Modulus of rigidity of a given wire by oscillating method

1. GROUP-B
AREEBA FATHA ALI 12 ANEESA ARIF
14
HAMEEZA SAEED 24
UMM-E-HANI 26
TANIA CH 02
SAFFA MARYAM 03
FAREEHA SHABBIR 20
SEHRISH SARWAR 21

3. PROJECT TOPIC
Determination of modulus of rigidity of a material
of a given wire by oscillating method

4. PURPOSE OF PRCTICAL
To find the MODOLUS OF RIGIDITY OF WIRE when a
heavy body is supported by it and execute torsional head.

5. APPARATUS
• Solid Cylindrical Rod
• Suspension Wire
• Tortion Head
• Stop Watch
• Vernier Callipers
• Screw Guage
• Mass Balance
• Meter Rod
• Knitting Needle
• Stand

6. THEORY
MODULUS OF RIGIDTY:
Within the elastic limit, the ratio of shearing stress to
shearing strain is called MODOLUS OF RIGIDITY.
• Unit of modulus of rigidity is n/𝐦 𝟐
• FORMULA is Y=
𝑭/𝑨
𝒕𝒂𝒏Ө

7. THEORY
• STRESS:
THE FORCE APPLIED ON THE UNIT AREA TO PRODUCE ANY
CHANGE
IN THE SHAPE, LENGTH AND SHAPE OF THE BODY
STRESS =
𝑭𝑶𝑹𝑪𝑬 (𝑭)
𝑨𝑹𝑬𝑨(𝑨)
UNIT: N𝒎−𝟐
• STRAIN:
STRAIN IS THE MEASURE OF THE DEFORMATION OF THE
SOLID WHEN STRESS IS APPLIED TO IT
IN CASE OF DEFORMATION IN ONE DIMENSION STRAIN IS
DEFINED AS A FRACTIONAL CHANGE IN LENGTH
STRAIN (Ɛ) =∆𝑙/𝑙
UNIT UNITLESS

8. THEORY
SHEARSTRESS:
When two equal and opposite forces are applied
tangentially to the cross section of the body .The stress induced is known as
SHEAR STRESS.
SHEARSTRAIN:
SHEAR STRAIN is defined as the strain accompanying a
shearing action.It is the angle in radian measure through which the body
gets distorted when subjected to an external shearing action.

9. PROCEDURE
We perform following steps in doing this EXPERIMENT …..
1. Measure the MASSof
Cylindricalrod by using
digital mass balance.
2. Measure the mean DIAMETER
of Suspension wire by using
Screw Gauge.
DIAMETER (𝒅)

10. 3.Find the RADIUS of the wire
𝒓 = 𝒅/𝟐
4.FIND THE Measure the
DIAMETER of Cylindrical Rod
by using Vernier Caliper
diameter(d)
5.Find the RADIUS of the
cylindrical rod
r=d/2

11. 6.Find the length of SUSPENSION
WIRE and length of rod (l) by
using METER ROD
7. Calculate the time for
10 vibrations
a) t1 for first time
b) t2 for second time
c) t =
𝑡1+𝑡2
2
8. Calculate TIME PERIOD as
T=t/10

12. DIAGRAM

13. • Calculate modulus of rigidity by using this formula.….
η= 2∏mL(3R2+ 4L2)/3r4T2
UNIT: dynes/cm 𝟐
Sr. No Vibrations Time fore 10
vibrations
(s)
Time period
T=t/10
(s)
1 10 16.50 1.650
2 10 16.53 1.653
3 10 16.38 1.638

14. OBSERVATIONS
• LENGTH OF ROD = L = 25.5 cm
• MASS OF ROD = m =587.3 cm
• MEAN DIAMETER OFD WIRE = d = 0.427 mm =
0.0427 cm
• MEAN RADIUS OF WIRE = 0.2135 cm
• LENGTH OF WIRE = 59.5 cm
• MEAN DIAMETER OF ROD = D= 19.006 mm =
1.9006 cm
• MEAN RADIUS OF ROD = R =0.9503 cm

15. RESULT
• The MODULUS OF RIGIDITY of wire calculated by using solid cylindrical
rod is
1.48 × 1014
dynes/𝑐𝑚2