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प्रश्न
A bullet of mass m moving at a speed v hits a ball of mass M kept at rest. A small part having mass m breaks from the ball and sticks to the bullet. The remaining ball is found to move at a speed v1 in the direction of the bullet. Find the velocity of the bullet after the collision.
उत्तर
Given:
The mass of bullet moving with speed v is m.
The mass of the ball is M and it is at rest.
m' is the fractional mass of the ball that sticks with the bullet.
The remaining mass of the ball moves with the velocity v1.
Let v2 be the final velocity of the bullet plus fractional mass system.
On applying the law of conservation of momentum, we get:
mv + 0 = (m' + m)v2 + (M − m') v1
\[\Rightarrow v_2 = \frac{mv - (M - m') v_1}{m + m'}\]
Therefore, the velocity of the bullet after the collision is \[\frac{mv - (M - m') v_1}{m + m'}\]
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