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Two bodies of...

Question

Two bodies of masses $m_{1}$ and $m_{2}$ are acted upon by a constant force $F$ for a time $t$ . They start from rest and acquire kinetic energies $E_{1}$ and $E_{2}$ respectively. Then $\frac{E_{1}}{E_{2}}$ is

\frac{m_{1}}{m_{2}}

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\frac{m_{2}}{m_{1}}

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\frac{\sqrt{m_{1} m_{2}}}{m_{1} + m_{2}}

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Solution

The correct option is B $\frac{m_{2}}{m_{1}}$
Bodies of mass $m_{1}$ and $m_{2}$ acted on by force F (say) for time t. Acceleration in mass $m_{1}$ = $\frac{F}{m_{1}}$
Acceleration in mass $m_{2}$ = $\frac{F}{m_{2}}$
Velocity acquired during this time for mass $m_{1}$
$v_{1} = \frac{F}{m_{1}} t$
Velocity acquired during this time for mass $m_{2}$
$v_{2} = \frac{F}{m_{2}} t$
Ratio of kinetic energy acquired
$\frac{E_{1}}{E_{2}} = \frac{\frac{1}{2} m_{1} v_{1}^{2}}{\frac{1}{2} m_{2} v_{2}^{2}}$
$\frac{E_{1}}{E_{2}} = \frac{m_{1} \times (\frac{F}{m_{1}} t)^{2}}{m_{2} \times (\frac{F}{m_{2}} t)^{2}}$
$\frac{E_{1}}{E_{2}} = \frac{m_{2}}{m_{1}}$

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