Question

A solid cylinder of mass $m$ and radius R is placed on rough plank of mass $m$ which is further placed on a frictionless surface. There is no sliding of cylinder over plank. If horizontal force F is applied on plank then

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

Answer 1

Answer: (A), (B), (C)

The correct options are
A Acceleration of cylinder is $\frac{F}{4m}$
B Acceleration of plank is $\frac{3F}{4m}$
C Friction force is $\frac{F}{4}$


$F-f=m{a}_p,f=m{a}_c,f\text{/}R=\frac{m\text{/}{R}^2}{2}\alpha$

Also $a_c+R\alpha =a_p$ (pure rolling)

$a_c+\frac{2f}{m}=a_p\Rightarrow a_c+2a_c=a_p\Rightarrow 3a_c=a_p$

and $F-m{a}_c=m{a}_p\Rightarrow F=m(a_c+a_p)$

$\frac{F}{m}=a_c+3a_c\Rightarrow a_c=\frac{F}{4m}f=m{a}_c=\frac{F}{4}$

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