Question

A long block A of mass M is at rest on a smooth horizontal surface. A small block B of mass $M/2$ is placed on A at one end and projected along A with some velocity v. The coefficient of friction between the block is $\mu$. Then, the accelerations of blocks A and B before reaching a common velocity will be respectively.

• A. $\frac{\mu g}{2}$ towards right), $\frac{\mu g}{2}$(towards left)
• B. $\mu g$ (towards right), $\mu g$(towards left)
• C. $\frac{\mu g}{2}$(towards right), $\mu g$(towards left)
• D. $\mu g$(towards right), $\frac{\mu }{2}$(towards left)

Answer 1

Answer: (C)

$\frac{\mu g}{2}$(towards right), $\mu g$(towards left)

The force causing the motion of A is frictional force between A and B,
So, acceleration of A
$\mu M_{B}g=M_A{a}_A$
$\Rightarrow a_A=\mu \left(\frac{M_a}{M_A}\right)g=\frac{\mu g}{2}$(towards right)
Block B experiences frictions force toward left
$M_B{a}_B=\mu M_{B}g\Rightarrow a_B=\mu g$ towards left.