A disc of mass m and radius R is placed over a plank of same mass m. There is sufficient friction between disc and plank to prevent slipping. A force F is applied at the centre of the disc.

Force of friction between the disc and the plank is

Options

A. `F/2`
B. `F/4`
C. `F/3`
D. `(2F)/3`

Answer

B

Explanation

`F-f= ma_(1)`………..(1)
`f=ma_(2)`……..(2)
`alpha = tau/I = (fR)/(1/2mR^(2)) = (2f)/(mR)`……….(3)
`a_(1)-Ralpha = a_(2)`…………(4)
Solving these four equations, we get `a_(1) = (3F)/(4m), a_(2) = F/(4m), f=F/4, alpha = F/(2mR)`