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Q.

A uniform cylindrical disc of radius $R$ and mass $M$ is pulled over a horizontal frictionless surface by a constant force. The force is applied by means of a string wound around the disc as shown in the figure. If it starts from rest at $t = 0$ , the linear and angular displacements respectively at time $t$ are :

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a

$(\frac{2 F}{M}) t^{2}, (\frac{2 F}{M R}) t^{2}$

b

$(\frac{F}{2 M}) t, (\frac{F}{2 M R}) t^{2}$

c

$(\frac{F}{2 M}) t^{2}, (\frac{F}{M R}) t^{2}$

d

$(\frac{F}{M}) t^{2}, (\frac{F}{M}) t^{2}$

answer is C.

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Detailed Solution

$a = \frac{F}{M}; s = \frac{1}{2} a t^{2} = \frac{1}{2} \frac{F}{M} t^{2} α = \frac{τ}{I} = \frac{F R}{\frac{M R^{2}}{2}} = \frac{2 F}{M R} \Rightarrow θ = \frac{1}{2} α t^{2} = \frac{1}{2} \times \frac{2 F}{M R} \times t^{2} = \frac{F t^{2}}{M R}$

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