Question

Two balls of mass 2 kg and 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet, the ratio of their kinetic energy will be___. Neglect air resistance in both the cases.

• A. $1:1$
• B. $2:3$
• C. $1:2$
• D. $\sqrt{2}:1$

Answer 1

The correct option is C

$1:2$

When an object falls under gravity, its speed at any instant does not depends on its mass. The speed of both the masses will be the same when they are at 30 feet from the top of the building because they are experiencing the same acceleration(g).
We know that, kinetic energy, K.E= $\frac{1}{2}m{v}^2$
Let $m_1$ be the mass of first ball = $2kg$ and $m_2$ be the mass of second ball = $4kg$.
Let the speed of both the balls be v.
Let $K.E_1$ and $K.E_2$ be the kinetic energies of the first and second ball, respectively.

$\frac{(K.E{)}_1}{(K.E{)}_2}$$=\frac{\frac{1}{2}{m}_1{v}^2}{\frac{1}{2}{m}_2{v}^2}=\frac{m_1}{m_2}=\frac{2}{4}$
$\Rightarrow$ $(K.E{)}_1:(K.E{)}_2=1:2$
$\therefore$ The required ratio is 1:2.