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Question

In given figure, pulley having radius, r=1 m and moment of inertia I=2 kgm2 about its axis of rotation. If T1=4 N and T2=2 N are the tension in the strings. Find the angular acceleration of pulley. (Take anti-clockwise rotation +ve)

A
2 rad/s2
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B
1 rad/s2
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C
4 rad/s2
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D
3 rad/s2
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Solution

The correct option is B 1 rad/s2
F. B. D of Pulley


Net torque on Pulley about axis of rotation
τnet=(T1T2)r
(Taking anticlockwise rotation +ve)

τnet=(42)×1
=2 Nm

Given: (I=2 kg-m2)
We also know,
τ=I×α
τnet=I×α
α=τnetI=22=1 rad/s2

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