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A constant force (F) is applied on a stationary particle of mass ‘m’. The velocity attained by the particle in a certain displacement will be proportional to

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1/m

$\sqrt{3}$

1/ $\sqrt{m}$

answer is D.

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Detailed Solution

$m \frac{d v}{d t} = F \Rightarrow m \frac{d x}{d t} \frac{d v}{d x} = F$

$\Rightarrow \int_{0}^{v} v \cdot d v = \frac{F}{m} \int_{0}^{s} d x$

$\Rightarrow \frac{v^{2}}{2} = \frac{F}{m} s$

$\Rightarrow v \propto \sqrt{s}$

$a n d, v \propto \frac{1}{\sqrt{m}}$

$alternatively : a = \frac{F}{m} \Rightarrow v^{2} = 2 as = 2 \frac{F}{m} s$

$\Rightarrow v \propto \sqrt{s}$

$a n d, v \propto \frac{1}{\sqrt{m}}$

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