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प्रश्न
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.
संख्यात्मक
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उत्तर
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
\[ v_{P} : v_{Q} = 3 : 1 \]
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