First slide

Law of conservation of momentum and it's applications

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

Moderate

A

15 m/sec downwards
B

15 m/sec upwards
C

51 m/sec downwards
D

51 m/sec upwards

Solution

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 in 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
$P_{initial} = P_{final}$
$\Rightarrow 2500 = 20 \times 150 + 30 \times V \Rightarrow V = - 15 m / s$
i.e. it moves in downward direction.

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