First slide

Rolling motion

Question

A force F acts tangentially at the highest point of a disc of mass m kept on a rough horizontal plane. If the disc rolls without slipping, the acceleration of centre of the disc is:

Moderate

A

$\frac{2 F}{3 m}$
B

$\frac{10 F}{7 m}$
C

$zero$
D

$\frac{4 F}{3 m}$

Solution

$\begin{array}{l} F + f = m a . . . . . . (i) \\ F R - f R = \frac{m R^{2}}{2} \frac{a}{R} . . . . . . (i i) \\ F - f = \frac{m a}{2} . . . . . . . . (i i i) \\ 2 F = \frac{3 m a}{2} \Rightarrow a = \frac{4 F}{3 m} \end{array}$

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