Question

If the units of ML are doubled, then the unit of kinetic energy will become :

• A. 8 times
• B. 16 times
• C. 4 times
• D. 2 times

Answer 1

The correct option is A 8 times

Kinetic energy is defined as $E=\frac{1}{2}m{v}^2$
Dimensions of kinetic energy $E=\left[M{L}^2{T}^{-2}\right]$
$\therefore$ $\frac{E^{\prime }}{E}=\frac{\left[\right(M^{\prime }\left)\right(L^{\prime }{)}^2\left(T{)}^{-2}\right]}{\left[M{L}^2{T}^{-2}\right]}=\frac{\left[\right(2M\left)\right(2L{)}^2(T{)}^{-2}]}{\left[M{L}^2{T}^{-2}\right]}=8$
Thus if the units of M and L are doubled, then the unit of kinetic energy will become $8$ times.