Question

The kinetic energy of the body will become eight times if

• A. Its mass is made four times
• B. Its velocity is made four times
• C. Both the mass and velocity are doubled
• D. Both the mass and velocity are made four times

Answer 1

The correct option is C

Both the mass and velocity are doubled

The kinetic energy in terms of mass and velocity is,

$\Rightarrow K.E=\frac{1}{2}m{v}^2$

Let the mass and the velocity of the body be doubled, then, the kinetic energy becomes,

$$\begin{gathered} \Rightarrow K.E=\frac{1}{2}2m\times {\left(2v\right)}^2 \\ \Rightarrow K.E=\frac{1}{2}\times 8m{v}^2 \\ \Rightarrow K.E=8\times \frac{1}{2}m{v}^2 \\ \Rightarrow K.E=8K.E \end{gathered}$$

Thus, the kinetic energy of the body will become eight times when velocity and mass are doubled.

Hence, option C is the correct answer.