Question

A ball of mass $2 kg$ and another of mass $6 kg$ are dropped together from a $80$ feet tall building. After a fall of $50$ feet each towards the earth, their respective kinetic energies will be in the ratio of

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

Answer 1

Answer: (A)

Decrease in P.E = Gain in K.E energies.
$m g\left(h_{1}-h_{2}\right)=k_{f}-k_{i} \quad\left(k_{i}=0\right)$
$\frac{m_{1} g\left(h_{1}-h_{2}\right)=k_{f_{1}}}{m_{2} g\left(h_{1}-h_{2}\right)=k_{f_{2}}} \Rightarrow \frac{m_{1}}{m_{2}}=\frac{k_{f_{1}}}{k_{f_{2}}} \Rightarrow \frac{1}{3}=\frac{k_{f_{1}}}{k_{f_{2}}}$