Question 55: Centre of Mass and Rotational Motion

Question

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A):  Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_{\mathrm{A}}=5 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}, v_{\mathrm{C}}=4 \mathrm{~m} / \mathrm{s}$. If we wait sufficiently long for elastic collision to happen, then $v_{\mathrm{A}}=4 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}$, $v_{\mathrm{C}}=5 \mathrm{~m} / \mathrm{s}$ will be the final velocities.
Reason (R): In an elastic collision between identical masses, two objects exchange their velocities.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

We know that two bodies of the same mass exchange their velocities after an elastic head-on collision.
Given, initially,
Here, $${V_{AB}} = {v_A} - {v_B} = 5 - 2 = 3\,m/s$$
$${V_{CB}} = {v_C} - {v_B} = 4 - 2 = 2\,m/s$$
first A will collide with B and the velocities will be exchanged.
i.e. now, V$_A$ = 2 m/s and V$_B$ = 5 m/s and V$_C$ = 4 m/s
As $V_B > V_C$
So, B will collide and exchange the velocities with C.
So, $V_B=4$ m/s. and $V_C=5$ m/s.
Hence, finally,
$$\eqalign{
  & {V_A} = 2\,m/s  \cr 
  & {V_B} = 4\,m/s  \cr 
  & {V_C} = 5\,m/s \cr} $$
So, A is false but R is true.

Answer

Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

Answer

Both (A) and (R) are true and (R) is the correct explanation of (A)

Answer

(A) is false but (R) is true

Answer

(A) is true but (R) is false

Centre of Mass and Rotational Motion

Choose the correct answer: