Question

A block of mass $m_1$ kg is horizontally thrown with a velocity of 10m/s on a stationary long plank of mass 2kg whose surface has a $\mu =0.5$. The plank rests on frictionless surface. Find the time when $m_1$ comes to rest w.r.t. plank.

• A. 4/3 sec
• B. 3/4 sec
• C. 8/3 sec
• D. 3/8 sec

Answer 1

The correct option is A 4/3 sec

There will be friction force between mass and plank until both mass and plank has same velocity.
Let the block be going in forward direction initially, so the frictional force on it will be in backward direction and on plank will be in forward direction.
Normal force between block & plank is $1\times g=10N$
Frictional Force will be $\mu N=0.5\times 10=5N$
Deceleration of block will be $\frac{5}{1}=5$ and acceleration of plank will be $\frac{5}{2}=2.5$
Final speed of both plank & block are equal, so
$v=u+atv=0+2.5t=10-5t10=7.5tt=\frac{4}{3}s$