Question 26

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 $$v_A = 5\,\text{m/s},\; v_B = 2\,\text{m/s},\; v_C = 4\,\text{m/s}$$. If we wait sufficiently long for elastic collision to happen, then $$v_A = 4\,\text{m/s},\; v_B = 2\,\text{m/s},\; v_C = 5\,\text{m/s}$$, 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 :

Solution

When 2 bodies of the same mass undergo elastic collision, their velocities get exchanged.

In the given system, since ball A is faster than ball B, which is slower than ball C, first ball A and ball B will collide and exchange their velocities.

$$v_{A,\ final}=2$$ m/s and $$v_B'=5$$ m/s

Then, ball B and ball C will collide and exchange their velocities

$$v_{B,\ final\ }=4$$ m/s and $$v_{c,\ final\ }=5$$

Therefore, final velocities of the balls are $$v_{A,\ final}=2$$ m/s, $$v_{B,\ final\ }=4$$ m/s and $$v_{c,\ final\ }=5$$

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