Consider the system shown. A solide sphere (of mass m and radius R) is placed over a plak (of mass 2m and placed over a smooth horizontal surface.) A horizontal force F is applied at the top of the sphere, as shown. Consider that the friction between the sphere and plank is sufficient enough for no slipping of the sphere over then plank.

Acceleration of the plank is

Options

A. `(3F)/(16 m)`
B. `(11F)/(8m)`
C. `(9F)/(4m)`
D. Zero

Answer

A

Explanation

`f = 2ma` ....(1)
`a_(cm) = a + alpha R` ....(2)
`tau_(0) = I_(0) alpha`
`F + f = (2)/(5) m R alpha`....(3)
`F - f - ma = ma_(cm)` .........(4)
on solving
`a_(cm) = (22 alpha R)/(25)`......(7)
`alpha = (25F)/(16 mR)`
`a = (-3F)/(16m)`
and `f = 2 ma`
`f = 2 xx m xx - (-3F)/(16m)`
`f = - (3F)/(8)`
Here -ve sign indicates that the direction is opposite.