Question

On increasing the speed of a body to $2m{s}^{-1}$, it's kinetic energy is quadrupled. Then, its original speed must be:

• A. $0.25m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $4m{s}^{-1}$
• D. $2m{s}^{-1}$

Answer 1

The correct option is B $1m{s}^{-1}$

Let $K=\frac{1}{2}M{V}^2$

On increasing speed to $2m{s}^{-1}$.

$K^{\prime }=\frac{1}{2}M\times 2^2=4\times K$

$\Rightarrow \frac{1}{2}M4=4\times \frac{1}{2}M{V}^2$

$\Rightarrow V=1m/s$