If an ivory ball of mass 2m moving with a velocity ‘v’ strikes head on to a close row of three identical ivory balls each of mass m as shown in the figure. Then after the collisions which may be assumed as elastic, which of the following occur?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

The balls numbered 2 and 3 will move with velocity v, the others staying at rest.

The ball numbered 3 will move with velocity 2v, all others staying at rest.

The ball numbered 3 moves with velocity 4v/3 and the striking ball moves with velocity v/3.

The balls numbered 1, 2 and 3 move with velocity v/3 and the striking ball stops dead.

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$m_{1} = 2 m; m_{2} = m_{3} = m_{4} = m$

$\begin{array}{l} u_{1} = V f o r m; u_{2} = o f o r m_{2} \\ V_{1} = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1} + \frac{2 m_{2} u_{2}}{m_{1} + m_{2}} \\ = \frac{m \times V}{3 m} + o \\ \Rightarrow V_{1} = \frac{V}{3} \\ V_{2} = \frac{2 m_{1} u_{1}}{m_{1} + m_{2}} + (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) u_{1} \\ = \frac{2 m_{1} V}{3 m} \\ = \frac{4 m V}{3 m} \\ \Rightarrow V_{2} = \frac{4}{3} V \end{array}$