Question

A long block A is at rest on a smooth horizontal surface. A small block B whose mass is half of mass of A is placed on A at one end and is given an initial velocity u as shown in Fig. 8.274. The coefficient of friction between the blocks is $\mu$.

• A. Finally both move with a common velocity 2u/3.
• B. Acceleration of B relative to A initially is $3\mu g/2$ towards left.
• C. Magnitude of total work done by friction is equal to the final kinetic energy of the system.
• D. The ratio of initial to final momentum of the system is 1.

Answer 1

Answer: (B), (D)

The correct options are
B Acceleration of B relative to A initially is $3\mu g/2$ towards left.
D The ratio of initial to final momentum of the system is 1.

$v$ is the final common velocity.
$(m+2m)v=mu\Rightarrow v=\frac{u}{3}$
$a_1=\frac{\mu mg}{m}=\mu g,a_2=\frac{\mu mg}{2m}=\frac{\mu g}{2}$
Acceleration of $B$ relative to $A$:
$a_1+a_2=\mu g+\frac{\mu g}{2}$
$=\frac{3}{2}\mu g$ towards left
Work done against friction:
$W_i=K_i-K_f=\frac{1}{2}m{u}^2-\frac{1}{2}3m{v}^2=\frac{m{u}^2}{3}$
Final $KE=\frac{1}{2}3m{v}^2=\frac{m{\mu }^2}{6}$
Hence, $c.$ is not correct.
Option (d) is correct because momentum is always conserved as there is no external force.