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Two bodies of equal masses 1kg are collided. After collision one of the bodies is moving with a velocity of $4 {ms}^{- 1}$ . If the total KE of system after collision is 12.5 J, then velocity of second body is

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${3ms}^{- 1}$

${30ms}^{- 1}$

${20ms}^{- 1}$

${2ms}^{- 1}$

answer is A.

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Detailed Solution

$m_{1} = m_{2} = {1Kg, v}_{1} = {4m/s, v}_{2} = ?$

$\Rightarrow \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2} = 12.5J$

$\Rightarrow \frac{1}{2} \times 1 \times {(4)}^{2} + \frac{1}{2} \times m_{2} \times v_{2}^{2} = 12.5J$

$\Rightarrow \frac{1}{2} \times {(4)}^{2} + \frac{1}{2} \times 1 \times v_{2}^{2} = 12.5 J$

$\Rightarrow \frac{16}{2} + \frac{1}{2} v_{2}^{2} = 12.5 J$

$\Rightarrow \frac{1}{2} [16 + v_{2}^{2}] = 12.5 J$

$\Rightarrow 16 + v_{2}^{2} = 25$

$\Rightarrow v_{2}^{2} = 25 - 16 = 9$

$v_{2} = \sqrt{9} = 3 m/s$

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