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Question

A cotton reel of mass m and moment of inertia 2 kgm2 is kept at rest on a smooth horizontal surface. The reel has inner radius 0.2 m and outer radius 0.5 m. A horizontal force F=200 N starts acting as shown is the figure. Find the angular acceleration of the reel.

A
50 rad/s2
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B
20 rad/s2
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C
40 rad/s2
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D
100 rad/s2
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Solution

The correct option is B 20 rad/s2
Given,
Force acting on reel, F=200 N
Moment of inertia of reel about centre, I=2 kgm2
Radius of inner circle r=0.2 m
Radius of outer circle R=0.5 m

Due to force F, torque on the centre of the reel,
We can apply torque eqn about centre of mass of the reel,
τ=rFsinθ=rFsin90o
(θ=90o because force is acting perpendicular to the radius)

τ=0.2×200
τ=40 N-m

Also,
Torque, τ=Iα
τ=Iα=40 N-m
2 kgm2×α=40 N-m
α=20 rad/s2

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