Two bodies of masses 4kg and 16kg are at rest. The ratio of times for which the same force must act on them to produce the same kinetic energy in both of them is

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1 : 4

2 : 1

1 : 2

4 : 1

answer is C.

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Detailed Solution

a = F/m

$KE = \frac{1}{2} {mv}^{2} = \frac{1}{2} m {(at)}^{2} = \frac{1}{2} m {(\frac{F}{m} t)}^{2} = \frac{F^{2}}{2 m} t^{2}$

KE₁ = KE₂

$\frac{{t_{1}}^{2}}{2 m_{1}} = \frac{{t_{2}}^{2}}{2 m_{2}}$

$\frac{t_{1}}{t_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \sqrt{\frac{4}{16}} = \frac{1}{2}$

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