Q. A body of mass $50\ kg$ is projected vertically upwards with velocity of $100\ m/sec$. 5 seconds after this body breaks into $20\ kg$ and $30\ kg$. If $20\ kg$ piece travels upwards with $150\ m/sec$, then the velocity of the block will be
A) $15\ m/sec$ downwards
B) $15\ m/sec$ upwards
C) $51\ m/sec$ downwards
D) $51\ m/sec$ upwards
Explanation
(a) Velocity of $50\ kg$ mass after $5\ sec$ of projection
$v = u - gt = 100 - 9.8 \times 5 = 51\ m/s$
At this instant momentum of body is an upward direction
$P_{initial} = 50 \times 51 = 2550\ kg - m/s$
After breaking $20\ kg$ piece travels upwards with $150\ m/s$ let the speed of $30\ kg$ mass is $V$
$P_{final} = 20 \times 150 + 30 \times V$
By the law of conservation of momentum
$P_{initial} = P_{final}$
$\Rightarrow 2550 = 20 \times 150 + 30 \times V \Rightarrow V = - 15\ m/s$
$i.e.$ it moves in downward direction
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.