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Question

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

A
25 rad s2
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B
20 rad s2
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C
25 m s2
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D
20 m s2
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Solution

The correct option is A 25 rad s2
Given, m=3 kg, r=40 cm, F=30 N

Moment of inertia of hollow cylinder about its axis
=mr2=3×(0.4)2=0.48 kg m2

The torque is given by,
τ=Ia
Where, I= moment of inertia and a = angular accleration

In the given case
τ=rF, as the force is acting perpendicularly to the radial vector.
a=τI=Frmr2=Fmr=303×40×102a= 25 rad s2

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