Question

A disc of mass m and radius R is placed over a plank of mass m. There is sufficient friction between disc and plank to prevent slipping and there is no friction between plank and ground. A horizontal force F is applied at the centre of the disc, then

• A. Acceleration of the disc is $\frac{F}{2m}$
• B. Acceleration of the plank is $\frac{F}{2m}$
• C. Friction force between disc and plank is $\frac{F}{4}$
• D. Friction force between disc and plank is $\frac{F}{3}$

Answer 1

The correct option is C Friction force between disc and plank is $\frac{F}{4}$

$a_D$ and $a_P$ are the accelerations of the center of the mass of the disc and the plank.
Applying force equations to the disc and plank: $F-f=m{a}_D;f=m{a}_p$
Applying torque equations to disc: $fR=\frac{1}{2}m{R}^2\alpha$ Also the point of contact: $a_p=a_D-R\alpha$
$\frac{f}{m}=\frac{F-f}{m}-\frac{2f}{m};f=F-f-2f;$ $f=\frac{F}{4},a_p=\frac{F}{4m}and{a}_D=\frac{3F}{4m}$