Question

A ball of mass $2kg$ and another of mass $4kg$ are dropped together from a $60m$ tall building. After a fall of $30m$, their respective kinetic energies will be in the ratio of:

• A. $\sqrt{2}:1$
• B. $1:2$
• C. $2:1$
• D. $1:\sqrt{2}$

Answer 1

The correct option is B $1:2$

Given: mass of ball 1, $m_1=1kg$,
mass of ball 2, $m_2=4kg$,
height of building, $h=60m$.

Since the balls are dropped at the same time, the change in velocity is equal in ball 1 and ball 2. (As the balls fall with an acceleration due to gravity $10m{s}^{-2}$)

We know, kinetic energy $KE=\frac{1}{2}m{v}^2$
$\Rightarrow \frac{(K.E{)}_1}{(K.E{)}_2}=\frac{\frac{1}{2}{m}_1{v}^2}{\frac{1}{2}{m}_2{v}^2}$
$\Rightarrow \frac{m_1}{m_2}=\frac{2}{4}=\frac{1}{2}$
or, $(K.E{)}_1:(K.E{)}_2=1:2$