Question

As the speed of body becomes three times, its kinetic energy increases by _________.

• A. 3 times
• B. 9 times
• C. $\frac{1}{3}$ times
• D. $\frac{1}{9}$ times

Answer 1

The correct option is B

9 times

Given:

Let the previous speed of the body be $v$ and new speed be $v\text{'}$,

then $v\text{'}=3v$

Finding the new kinetic energy

Kinetic energy of a body is given by,

$KE=\frac{1}{2}m{v}^2$ (where m is the mass and v is the velocity of the body).

So the new kinetic energy of the body,

$KE\text{'}=\frac{1}{2}mv{\text{'}}^2$

$\Rightarrow KE\text{'}=\frac{1}{2}mx{\left(3v\right)}^2$

$\Rightarrow KE\text{'}=\frac{1}{2}mx{9v}^2$

$\Rightarrow KE\text{'}=9x\left(\frac{1}{2}m{v}^2\right)$

$\Rightarrow KE\text{'}=9\times KE$

Hence, kinetic energy increases by 9 times.

Hence, option (b) is correct.