Question

A long plank of mass 2 kg is placed on a smooth horizontal surface. Two blocks each of mass 1 kg are placed in contact on its rough surface. The coefficient of friction between first block and plank is 0.2 and that between second block and plank is 0.4. The blocks are projected in the opposite direction on the plank with velocity 2 m/s and 6 m/s respectively. The velocity of plank when both the blocks come to relative rest with respect to the plank and total work done by friction on the system (blocks + plank) will be

• A. 2 m/s, 18 J
• B. 1 m/s, zero
• C. 1 m/s, 18 J
• D. 2 m/s, 30 J

Answer 1

Answer: (C)

1 m/s, 18 J

Linear momentum conservation

$\Rightarrow +1\left(6\right)-1\left(2\right)=(1+1+2)v$

$v=1m/s$

$w_f=k_f-k_i$

$=\frac{1}{2}\times 4\times 1^2-\frac{1}{2}\times 1\times 2^2-\frac{1}{2}\times 1\times 6^2$

$=-18j$