Topic: Engineering Mechanics
Two particles with masses in the ratio 1:4 are moving with equal kinetic energies. The magnitude of their linear momentums will conform to the ratio
- A. 1:8
- B. 1:2
- C. $\sqrt{2}:1$
- D. $\sqrt{2}$
Answer: B. 1:2
Explanation: Given $KE_{1} = KE_{2} \implies \frac{1}{2}m_{1}v_{1}^{2} = \frac{1}{2}m_{2}v_{2}^{2} \implies \frac{m_{1}}{m_{2}} = \left(\frac{v_{2}}{v_{1}}\right)^{2} \implies \frac{1}{4} = \left(\frac{v_{2}}{v_{1}}\right)^{2} \implies \frac{v_{1}}{v_{2}} = 2$. Ratio of momentum is $\frac{P_{1}}{P_{2}} = \frac{m_{1}v_{1}}{m_{2}v_{2}} = \left(\frac{1}{4}\right) \times 2 = \frac{1}{2}$.