First slide

Kinetic energy

Question

Two bodies of masses m and 4 m are moving with equal K.E. The ratio of their linear momenta is

Moderate

A

4:1
B

1:1
C

1:2
D

1:4

Solution

$(K.E.)_{1} = (K.E.)_{2} Momentum P = \sqrt{2 mE} \propto \sqrt{m} ∴ \frac{P_{1}}{P_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \sqrt{\frac{m}{4 m}} = \frac{1}{2} P_{1} : P_{2} = 1 : 2$

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