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

v is the final common velocity.

$(\mathrm{m}+2\mathrm{m})\mathrm{v}=\mathrm{mu}\Rightarrow \mathrm{v}=\frac{\mathrm{u}}{3}$

${\mathrm{a}}_1=\frac{\mathrm{\mu mg}}{\mathrm{m}}=\mathrm{\mu g},{\mathrm{a}}_2=\frac{\mathrm{\mu mg}}{2\mathrm{m}}=\frac{\mathrm{\mu g}}{2}$

Acceleration of B relative to A: 

${\mathrm{a}}_1+{\mathrm{a}}_2=\mathrm{\mu g}+\frac{\mathrm{\mu g}}{2}=\frac{3}{2}\mathrm{\mu g}$ towards left

Work done against friction:

${\mathrm{W}}_1={\mathrm{K}}_{\mathrm{i}}-{\mathrm{K}}_{\mathrm{f}}=\frac{1}{2}{\mathrm{mu}}^2-\frac{1}{2}3{\mathrm{mv}}^2=\frac{{\mathrm{mu}}^2}{3}$

Final $\mathrm{KE}=\frac{1}{2}3{\mathrm{mv}}^2=\frac{{\mathrm{mu}}^2}{6}$

Hence, 3 is not correct.

Option (4) is correct, because momentum is always conserved as there is no external force.