Question

The ratio of work done by the internal forces of a car in order to change its speed from $0$ to $V$ and from $V$ to $2V$ is (Assume that the car moves on a horizontal road)

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

$\frac{1}{3}$

Work-Energy Theorem

$Work=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

So,
$\frac{W_1}{W_2}=\frac{\frac{1}{2}m{v}^2-\frac{1}{2}m[0{]}^2}{\frac{1}{2}m[2v{]}^2-\frac{1}{2}m[v{]}^2}$

$=\frac{\frac{1}{2}m{v}^2}{3\times \frac{1}{2}m{v}^2}$

$=\frac{1}{3}$