A body of mass 10 kg moving with a velocity of $5 m s^{- 1}$ hits a body of 1 gm at rest. Find the velocity of the second body after collision assuming it to be perfectly elastic ?

10 m s^{- 1}

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5 m s^{- 1}

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15 m s^{- 1}

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0.10 m s^{- 1}

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Solution

The correct option is A $10 m s^{- 1}$
For a perfectly elastic collision, coefficient of restitution is $e = 1$ .

Let $u$ and $v$ be the velocities of $10 kg$ and $1 g$ masses after collision.

Thus, $e = \frac{rel. vel.of separation}{rel. vel. of approach} = \frac{v - u}{5 - 0} = \frac{v - u}{5}$

But, as $e = 1$ , we have $v - u = 5$ .

Total momentum before collision is $P = 10 \times 5 = 50 kg m/s$
Total momentum after collision is $P = 10 \times (v - 5) + 0.001 \times v = 10.001 v - 50$

Thus, $10.001 v - 50 = 50 \Rightarrow v = \frac{100}{10.001} \approx 10 m/s$

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A body of mass 10 kg moving with a velocity of 5ms−1 hits a body of 1 gm at rest. Find the velocity of the second body after collision assuming it to be perfectly elastic ?

A body of mass 10 kg moving with a velocity of $5 m s^{- 1}$ hits a body of 1 gm at rest. Find the velocity of the second body after collision assuming it to be perfectly elastic ?