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Center of Mass

Section: Physics

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Question : 1 of 18

Marks: +1, -0

A body moving along a straight line collides another body of same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is 0.5 , then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional)

[AP EAPCET 24 May 2025 S1]

$2:5$
$2:3$
$5:7$
$3:7$

Solution:

Let initial velocities are

u

and

\; \frac{u}{2}

and final velocities are

v_A

and

v_B

. Then, momentum is conserved,

m u + \frac{m u}{2} = m v_A + m v_B

or

v_A + v_B = \frac{3 u}{2}

Coefficient of restitution is 0.5 ,

\Rightarrow e = \frac{v_B - v_A}{u_A - u_B} = \frac{v_B - v_A}{u - \left(\frac{u}{2}\right)}

\Rightarrow v_B - v_A = \frac{u}{4} \ldots (ii)

From (i) and (ii)

v_B = \frac{7}{8} \cdot u

And from (i) and (iii)

v_A = \frac{5}{8} u

Hence, ratio

\frac{v_A}{v_B} = \frac{\frac{5}{8}}{\frac{7}{8}} = \frac{5}{7}

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