Question

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 other block will be

• A. 15 m/sec downwards
• B. 15 m/sec upwards
• C. 51 m/sec downwards
• D. 51 m/sec upwards

Answer 1

Answer: (A)

15 m/sec downwards

Answer 2

Velocity of 50 kg. mass after 5 sec of projection $v = u - g t$ $= 100 - 9.8 \times 5 = 51 \mathrm {~m} / \mathrm { s }$

At this instant momentum of body is in upward direction

$P _ { \text {initial } } = 50 \times 51 = 2550 \mathrm {~kg} - \mathrm { m } / \mathrm { s }$

After breaking 20 kg piece travels upwards with 150 m/s let the speed of 30 kg mass is V

$P _ { \text {final } } = 20 \times 150 + 30 \times V$

By the law of conservation of momentum

⇒ $2550 = 20 \times 150 + 30 \times V \Rightarrow V = - 15 \mathrm {~m} / \mathrm { s }$

i.e. it moves in downward direction.