GCE Kannur

1. Expt No:
Date:
TORSION TEST ON WIRES
AIM:
To determine the modulus of rigidity of material of steel wire.
APPARATUS:
Torsion wire, Wooden disc, Cylinders of known weight, Stopwatch &
Screw gauge.
PRINCIPLE:
Whenever a filament is twisted (thread, string, wire etc) forces come into
play that make it untwist. These are called torsional force. Weight suspended
from an elastic wire is in equilibrium and when it is twisted to one direction,
begins to oscillate about its equilibrium positon i.e., it becomes a torsional
pendulum.
t1 = 2π√(I1l / NJ)
t2 = 2π√(I2l / NJ)
t2
2
– t1
2
= 4π2
l [(I2 _ I1)/NJ]
Where,
I1 is the mass moment of inertia of the disc about the vertical axis through
the centre of the disc.
I2 is the mass moment of inertia of the disc about the vertical axis through
the centre of the disc with the cylindrical weights.
J is the polar moment of the wire.
t1 is the time for oscillation of the pendulum without cylindrical weights.
t2 is the time for one oscillation of the pendulum with cylindrical weights.
l is the length of pendulum.
w is the weight of one cylinder.
2a is the center-to-center distance between the cylinders.
r is the radius of the cylinder.
N is the modulus of rigidity of the material of the wire.
Where, I2 – I1 = 2w [a2
+ r2
/2]
N = 4π2
l / J [(I2 – I1)/(t2
2
– t1
2
)]

2. OBSERVATIONS & CALCULATIONS:
Length of wire, l =
Centre-to centre distance between cylinder, 2a =
a =
Least count (LC) of screw gauge =
Zero correction of screw gauge =
Table No:1 Measurement Of Diameter Of Wire
Corrected diameter of wire =
Polar moment of inertia of wire, J =
Table No:2 Measurement Of Diameter Of Cylindrical Weights
Weight (g)
Main scale
reading
Vernier
scale
reading
LC x VSR
Diameter
(cm)
Radius
(cm)
Least count of vernier caliper =
Radius of 55g cylinder, r1 =
Radius of 110g cylinder, r2 =
Diameter of disc, d =
Mass Moment of Inertia of discharge =
Calculation Of Modulus Of Rigidity Without Weight
Calculation Of Modulus Of Rigidity With Weight
Weight
(g)
Time for 20 oscillations, t2 (sec) Time
period,
t2 (sec)
N (GPa) Mean N
(GPa)1 2 3 Mean
Main scale
reading
Vernier scale
reading
LC X VSR Total (mm)
Diameter
(mm)
Time for 20 oscillations, t 1 (sec) Time period
1 2 3 Mean t1 (sec)

3. Diameter of the wire Free length between grips
0.4 mm to 0.7 mm 200dia
1 mm to 5 mm 100dia
5 mm to 12.5 mm 50dia
PROCEDURE:
1. Find the diameter of the wire in mm using screw gauge & weight of the
cylinder
weights.
2. Suspend the disc horizontally by the wire & clamp it on the stand.
3. Measure the length of the wire between the points of suspension & point of
oscillation.
4. Give a twist to the disc & allow it to oscillate.
5. When the oscillation becomes steady, start the stopwatch & note the time for
20
oscillations & calculate t1, period of oscillation.
6. Place the cylinder weights on the small roads fixed to the disc & find t2, i.e.
period of
oscillation with weights placed.
7. Repeat the experiment by changing the cylinder weights.
RESULT:
Modulus of rigidity of the material =
DISCUSSIONS: