Question

A body P has KE (E). Another body Q, whose mass is 9 times than P, also has kinetic energy (E). Calculate the ratio of velocities of P and Q.

Answer 1

Given, \[ m_{Q} = 9\, m_{P} \]

For the same kinetic energy,

\[ \frac{1}{2}\, m_{P} v_{P}^{2} = \frac{1}{2}\, m_{Q} v_{Q}^{2} \]

\[ m_{P} v_{P}^{2} = 9\, m_{P} v_{Q}^{2} \]

\[ v_{P}^{2} = 9\, v_{Q}^{2} \]

\[ v_{P} = 3\, v_{Q} \]

and the ratio is

\[ v_{P} : v_{Q} = 3 : 1 \]