Question

The velocity of a moving cart is reduced to \[ \frac{1}{3} \] rd of the initial velocity. Its kinetic energy is reduced by ______.

Options

• \[ \frac{1}{2} \]

• \[ \frac{1}{3} \]

• \[ \frac{1}{6} \]

• \[ \frac{1}{9} \]

Answer 1

The velocity of a moving cart is reduced to \[ \frac{1}{3} \] rd of the initial velocity. Its kinetic energy is reduced by \[ \underline{\frac{1}{9} }\].

Explanation:

If the velocity becomes v/3, then \[ K' = \frac{1}{9} \times \frac{1}{2}mv^{2} = \frac{1}{9}K \]. Thus kinetic energy is reduced to `1/9` of its initial value.