Question

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

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

Answer 1

The correct option is C. $1:2$.

When an object falls under gravity, its speed at any instant does not depend 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 same acceleration(g).

We know that, K.E= $\frac{1}{2}m{v}^2$
Let $m_1=2kg$ and $m_2=4kg$ and let speed of both the mass be v.
Let $K.E_1$ and $K.E_2$ be their kinetic energy respectively.

$\therefore$ $\frac{(K.E{)}_1}{(K.E{)}_2}=\frac{m_1}{m_2}=\frac{2}{4}$

$(K.E{)}_1:(K.E{)}_2=1:2$