Maxwell Needle Experiment physics honours

1. MAXWELL’S NEEDLE

2. AIM:-
To determine the modulus of rigidity of a
wire of some material using maxwell’s
needle.

3. APPARATUS REQUIRED:-
1. Maxwell Needle
2. Screw Gauge
3. Meter Scale
4. Weighing Machine
5. Stop Watch.
6. Knitting needle as a reference
7. Telescope as a point of viewing.

4. THEORY:-
Modulus of Rigidity:-
Modulus of Rigidity is basically the ratio of shear stress to the
displacement per unit sample length (shear strain).
More specifically,
modulus of rigidity (Shear Modulus) is the coefficient of
elasticity for a shearing force.
Modulus of Rigidity = Shear stress/Shear strain.

5. Maxwell’s needle is basically an empty hollow brass tube tied to a string.The
free end of string is attached to the fixed support.
In addition to this, there is a mirror present on the maxwell’ s needle which
helps in recording time period of oscillations.
We also have 2 solid cylinders and 2 hollow cylinders.
Diameters of all 4 cylinders are identical and slightly less compared to the
long brass rod.
The length of small 4 cylinders is L/4 ( where L is the length of long
cylinder.)
In the Maxwell’s needle experiment, 2 major configurations are used :-
Configuration 1 :-

6. Configuration 2 :-
For both these configurations time period is to be noted as shown in the
procedure.

7. 1- Here,
L = length of Maxwell Needle
l = length of wire.
M(s) = Mass of solid cylinder.
M(h) = Mass of hollow cylinder.
T1 = Time period in configuration-1
T2 = Time period in configuration -2
r = radius of wire

8. PROCEDURE:-
1. Measure the length of wire using meter scale through which the maxwell
needle is hanged . This will give you value of ‘l’.
2. Measure the length of maxwell needle wing meter scale . This will give you
value of ‘L’.
3. Measure the mass of both solid cylinders using balance and do its half, this
will give you value of M(s).
4. Measure the mass of both the hollow cylinders and do its half to get M(h).
5. Find out the least count of screw gauge and zero error in it.
6. Using screw gauge , measure the diameter of wire.(Observation table.)
7. Find out least count of stopwatch.
8. Now make the first configuration and oscillate it in horizontal plane about
vertical axis . Note the time for 20 oscillations using the knitting needle as
reference and using telescope for viewing.
[Note- the first oscillation is to be taken as 0th oscillation.]
9. Repeat the same thing for configuration-2.
10.Note the values , fill the observation table , put the values in the required
formula and hence calculate the modulus of rigidity.

9. Calculating time period for oscillations as instructed
in the following video…..

10. OBSERVATIONS:-
Calculating diameter of wire using screw gauge.
Mean diameter = 0.0475 cm
Mean radius = 0.02375 cm

11. Calculating time period for configuration 1 and 2 :-
Mass of solid cylinder = 250 grams.
Mass of hollow cylinder = 70 grams.
Length of wire = 54.5 cm.
Length of Maxwell Needle = 40 cm.

12. CALCULATIONS:-
Putting values
We get,
This
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13. RESULT:-
Hence,
Modulus of Rigidity of the given wire
comes out to be 0.830 × 10 ^ 11 N/m^2.
On seeing the table we find ,
The value of η corresponds to that of iron wrought
cast.
Therefore, we conclude material is Iron wrought.

14. PRECAUTIONS:-
1-There should be kink in the wire.
2-The maxwell needle should remain horizontal in the same plane .
3-the amplitude of oscillation should be small so that wire is not twisted
beyond elastic limit.
4-To avoid backless error, circular scale of screw gauge should be moved in
only one direction.
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