Question

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

• A. $ \sqrt{2}:1 $
• B. $ 1:4 $
• C. $ 1:2 $
• D. $ 1:\sqrt{2} $

Answer 1

Answer: (C)

In a free fall, two balls of different mass will acquire the same velocity after falling through same height.
From key idea, $v_{1}=v_{2}=v $ at a $30 \,ft$ from falling point.
Here, $m_{1}=2\, kg , m_{2}=4 \,kg$
Thus, $\frac{K_{1}}{K_{2}}=\frac{\frac{1}{2} m_{1} v^{2}}{\frac{1}{2} m_{2} v^{2}}$
$=\frac{m_{1}}{m_{2}}=\frac{2}{4}=\frac{1}{2}$