ExamBro
ExamBro
WBJEE · Physics · Center of Mass Momentum and Collision

There are \(n\) elastic balls placed on a smooth horizontal plane. The masses of the balls are \(m, \frac{m}{2}, \frac{m}{2^2}, \ldots . \frac{m}{2^{n-1}}\) respectively. If the first ball hits the second ball with velocity \(\mathrm{v}_0\), then the velocity of the \(\mathrm{n}^{\text {th }}\) ball will be,

  1. A \(\frac{4}{3} v_0\)
  2. B \(\left(\frac{4}{3}\right)^n v_0\)
  3. C \(\left(\frac{4}{3}\right)^{n-1} v_0\)
  4. D \(v_0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(\frac{4}{3}\right)^{n-1} v_0\)

Step-by-step Solution

Detailed explanation

Hint : 1st Collision \(\mathrm{V}_1=\frac{2 \times \mathrm{m}}{\frac{\mathrm{m}}{2}+\mathrm{m}} \mathrm{V}_0=\frac{4}{3} \mathrm{~V}_0\) 2nd Collision \(V_2=\frac{2 \times \frac{m}{2}}{\frac{m}{2}+\frac{m}{2^2}} \times V_0=\left(\frac{4}{3}\right)^2 V_0\) 3rd Collision…