Question

When velocity is halved, its kinetic energy becomes $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\text{th}$.

• A. True
• B. False

Answer 1

The correct option is A True

1. The energy possessed by a body, by virtue of its motion is called kinetic energy.
2. The kinetic energy $\left(k\right)$ is calculated by the formula $k=\frac{1}{2}m{v}^2$, where $m$is the mass and $v$is the velocity of the body.
3. Now, if the velocity of the body is halved, mass remains the same, the new kinetic energy obtained is written below:

$$\begin{gathered} k\text{'}=\frac{1}{2}m{\left(\frac{1}{2}v\right)}^2 \\ k\text{'}=\frac{1}{2}m·\frac{1}{4}{v}^2 \\ k\text{'}=\frac{1}{8}m{v}^2 \end{gathered}$$

4. The ratio of the kinetic energies can be written as shown below

$$\begin{gathered} \frac{k\text{'}}{k}=\frac{\frac{1}{8}m{v}^2}{\frac{1}{2}m{v}^2} \\ \frac{k\text{'}}{k}=\frac{1}{8}\times 2 \\ \frac{k\text{'}}{k}=\frac{1}{4} \end{gathered}$$

5. When velocity is halved, the new kinetic energy becomes $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\text{th}$.

Hence, the given statement is true.