The kinetic energy of a body is 100 J. If the mass is doubled and velocity is tripled, the new kinetic energy will be _____.

Given:
New mass, m'= 2m
New velocity, v'= 3V
Initial kinetic energy, KE= 100 J

To find: 
New Kinetic energy, K.E'

Solution: 
We know that,
KE = $\frac{1}{2}{\mathrm{mv}}^2$           ....(1)

$\mathrm{KE}\text{'}= \frac{1}{2}\mathrm{m}\text{'}\mathrm{v}{\text{'}}^2$

$\therefore \mathrm{KE}\text{'}= \frac{1}{2}\left(2\mathrm{m}\right){\left(3\mathrm{v}\right)}^2$

$\mathrm{KE}\text{'}= \left(2\right){{\left(3\right)}^2 \times \frac{1}{2}\mathrm{mv}}^2$

$\mathrm{KE}\text{'}=2\times 9 {\times \frac{1}{2}\mathrm{mv}}^2$

$\mathrm{KE}\text{'}=18 \mathrm{KE}$

$\therefore \mathrm{KE}\text{'}=18 \times 100= 1800 \mathrm{J}$

Therefore, the new kinetic energy will be 1800 J.