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A constant force starts acting on a body of mass m at rest. The velocity v acquired in traveling a specific distance depends on m as

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a

v $\propto$ m

b

$v \propto \frac{1}{\sqrt{m}}$

c

$v \propto \sqrt{m}$

d

v $\propto \frac{1}{m}$

answer is B.

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Detailed Solution

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u = 0, a = F/m, Apply $v^{2} = u^{2} + 2 a s$

$\Rightarrow$ $v^{2} = 0^{2} + \frac{2 F}{m} s$ $\Rightarrow$ $v^{2} = \frac{2 F s}{m}$

$\Rightarrow$ $v^{2} \propto \frac{1}{m}$ $\Rightarrow$ $v \propto \frac{1}{\sqrt{m}}$

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