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Q.

A moving mass of 1 kg collides elastically with a stationary mass of 2 kg. If E be the initial K.E. of the moving mass, the kinetic energy left with it after the collision will be

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a

0.80 E

b

0.64 E

c

0.36 E

d

0.08 E

answer is C.

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Detailed Solution

$v_{1} = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1} + (\frac{2 m_{2}}{m_{1} + m_{2}}) u_{2} = (\frac{8 - 2}{8 + 2}) u_{1} + 0 = \frac{6}{10} u_{1} (∵ u_{2} = 0) E = K . E before collisi o n = \frac{1}{2} \times 8 \times v_{1}^{2} = 4 u_{1}^{2} E_{1} = K . E . after collision = \frac{1}{2} \times 8 \times v_{1}^{2} = 4 \times {(\frac{6}{10} u_{1})}^{2} = \frac{36}{100} \times E_{1} = 0 \cdot 36 E$

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