The velocity of a moving cart is reduced to rd the initial velocity. Its kinetic energy is reduced by : 1. 2. 3. 4.

Reason Let initial velocity be v. Kinetic Energy at v = x m x v 2 = Kinetic Energy at = x m x = Hence, the kinetic energy is reduced by

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$\dfrac{1}{9}$

Reason — Let initial velocity be v.

Kinetic Energy at v = $\dfrac{1}{2}$ x m x v² = $\dfrac{\text{mv}^2}{2}$

Kinetic Energy at $\dfrac{\text{v}}{3}$ = $\dfrac{1}{2}$ x m x $(\dfrac{\text{v}}{3})^2$ = $\dfrac{1}{9}\Big(\dfrac{\text{mv}^2}{2}\Big)$

Hence, the kinetic energy is reduced by $\dfrac{1}{9}$

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