Question

Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is:_______.A. 1:9B. 1:3C. 1:1D.3:1E. 9:1

Answer 1

Answer:

D. 3 : 1

Explanation:

Let suppose that A and B are particles. From statement we know that $K_{A} = K_{B }$ (same kinetic energy) and $m_{A} = 9\cdot m_{B}$. Then,

$K_{A} = K_{B}$

$\frac{1}{2}\cdot m_{A}\cdot v_{A}^{2} = \frac{1}{2}\cdot m_{B}\cdot v_{B}^{2}$

$m_{A} \cdot v_{A}^{2} = m_{B}\cdot v_{B}^{2}$

$\frac{v_{B}}{v_{A}} = \sqrt{\frac{m_{A}}{m_{B}} }$

$\frac{v_{B}}{v_{A}} = 3$

And the ratio of the momentum of A to the momentum of B is:

$r = \frac{m_{A}\cdot v_{A}}{m_{B}\cdot v_{B}}$

$r = 9\times \frac{1}{3}$

$r = 3$

Hence, the correct answer is D.