Question

The K.E. of a body is increased most, by doubling its

• A. mass
• B. weight
• C. speed
• D. density

Answer 1

The correct option is C

speed

The explanation for correct option:

The correct option is C. speed.

1. Kinetic energy (K.E.) of a body is half of the product of its mass $m$ and square of its speed $v$.
2. $K.E.=\frac{1}{2}m{v}^2$
3. When the speed of a moving body is doubled, then kinetic energy becomes:
4. $\begin{array}{c}K.E.\text{'}=\frac{1}{2}m{\left(2v\right)}^2\\ =4\cdot \frac{1}{2}m{v}^2\\ =4K.E.\end{array}$
5. Thus, when speed is doubled, kinetic energy becomes four times.

The explanation for incorrect option:

A. mass

When the mass of a moving body is doubled, then kinetic energy becomes

$\begin{array}{c}K.E.\text{'}=\frac{1}{2}\left(2m\right)v^2\\ =2\cdot \frac{1}{2}m{v}^2\\ =2K.E.\end{array}$

Thus, when mass is doubled, the kinetic energy of the body is only doubled and not increased four times its initial value as in the case of doubling the speed.

B. weight

The kinetic energy of a body does not depend on its weight.

D. density

The kinetic energy of a body is not directly dependent on its density.

Thus, the K.E. of a body is increased most, by doubling its speed.