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JEE Main 2004 (AIEEE) · Work by a Variable Force

Work by a Variable Force question from JEE Main 2004 (AIEEE)

Q23JEE Main 2004 · AIEEEMedium

Work by a Variable Force

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

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Answer: (c)

Retardation $a = -kx$ , so $v\frac{dv}{dx} = -kx$ .
Loss of KE $= \int_0^x m k x\,dx = \frac{1}{2}mkx^2$
So loss of KE $\propto x^2$ ; the answer is (c).

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