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Q.

A body of mass 20 gm is moving with a certain velocity. It collides with another body of mass 80 gm at rest. The collision is perfectly inelastic. The ratio of the kinetic energies before and after collision of the system is:

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a

2 : 1

b

3 : 2

c

5 : 1

d

4 : 1

answer is C.

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Detailed Solution

$m_{1} u_{1} = (m_{1} + m_{2}) v \Rightarrow 20 u = (20 + 80) v \Rightarrow v = \frac{20}{100} u {KE}_{i} = \frac{1}{2} m_{1} {u_{1}}^{2}; \Rightarrow {KE}_{i} = \frac{1}{2} 20 u^{2} = 10 u^{2} \Rightarrow {KE}_{f} = \frac{1}{2} (m_{1} + m_{2}) v^{2} \Rightarrow {KE}_{f} = \frac{1}{2} (20 + 80) v^{2} \Rightarrow {KE}_{f} = \frac{1}{2} (20 + 80) {(\frac{20 u}{100})}^{2} = 2 u^{2} \frac{K . E ._{i}}{K . E ._{f}} = \frac{10 u^{2}}{2 u^{2}} = 5 : 1$

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