Question

A particle is moving in a straight line with retardation proportional to it's displacement. It's loss of kinetic energy for any displacement $X$ is proportional to

• A. $X^2$
• B. $e^X$
• C. $X$
• D. $lo{g}_e^X$

Answer 1

The correct option is A $X^2$

As particle is moving with retardation

$\therefore F=-kX$ Where k is the proportionality constant

Loss of $K.E=W.D$ $=\int -kX.dX$ $=\frac{-k{X}^2}{2}$

$\Rightarrow KE\propto X^2$