A solid sphere of mass 2 kg and radius 1m free to rotate about an axis passing through its centre. A constant tangential force ‘F’ is required to rotate the sphere with 10rad s^–1 in 2 s starting from rest. Then the value of F is

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10 N

2 N

4 N

answer is B.

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Detailed Solution

We know that $ω = ω_{ο} + αt$

From the given values,

$α = \frac{10}{2} = 5 rad / s^{2}$

Now the moment of inertia for solid sphere,

$I = \frac{2}{5} {MR}^{2} = \frac{4}{5}$

Torque,

$τ = Iα = rF$

$F = \frac{Iα}{R} = \frac{4}{5} \times 5 = 4 N$

Hence the correct answer is 4N.

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