A uniform disc of mass m and radius r rotates along an axis passing through its centre of mass and normal to its plane. An unstretchable rope is wound on the disc. Tangential acceleration of a point P on the periphery of the disc when a uniform force F is applied on the rope is

Options

A. `F/(2m)`
B. `(3F)/(2m)`
C. `F/m`
D. `(2F)/(m)`

Answer

D

Explanation

Using `tau = F r, tau = I alpha,` we get `Fr = I alpha = 1/2 mr^2 xx (a_t)/r` (where `a_t` is tangential acceleration)
`1/2 m a_t = F " " therefore a_t = (2F)/m`