Question

How is the kinetic energy of a moving cart affected if its velocity is reduced to $\frac{1}{3}$rd of the initial velocity?

• A. Kinetic energy reduces to $\frac{1}{3}$rd its initial value
• B. Kinetic energy increases to $\frac{1}{3}$rd its initial value
• C. Kinetic energy reduces to $\frac{1}{9}$th its initial value
• D. Kinetic energy increases to $\frac{1}{9}$th its initial value

Answer 1

The correct option is C

Kinetic energy reduces to $\frac{1}{9}$th its initial value

As we know kinetic energy $K=\frac{1}{2}m{v}^2$. Now, if the velocity $v$ is reduced to $\frac{1}{3}$rd of the initial velocity(keeping the mass same), the kinetic energy reduces to $\frac{1}{9}$th its initial value(since kinetic energy is directly proportional to the square of velocity).