Question

A ball of 4 kg mass and a speed os $3m{s}^{-1}$ has a head on elastic collision with 6 kg mass initially at rest. the speeds of both the bodies after collisiion are respectively.

• A. $0.6m{s}^{-1},2.4m{s}^{-1}$
• B. $-0.6m{s}^{-1},-2.4m{s}^{-1}$
• C. $-0.6m{s}^{-1},2.4m{s}^{-1}$
• D. $0.6m{s}^{-1},-2.4m{s}^{-1}$

Answer 1

Answer: (C)

$-0.6m{s}^{-1},2.4m{s}^{-1}$

Given

mass of ball $\left(m_1\right)$ is $4kg$

Velocity of ball $\left(v_1\right)$ is $3m/s$

another mass $m_2$ of $6kg$ having velocity $v_2$ is $0m/s$

For elastic collision external force is Zero therefore momentum is conserve before and after collision

Let velocity of $m_1$ and $m_2$ after collision is $v_3$ and $v_4$ respectively

Now

$m_1{v}_1+m_2{v}_2=m_1{v}_3+m_2{v}_4$

Substitute all value in above equation

$m_1{v}_1+m_2{v}_2=m_1{v}_3+m_2{v}_{4}4\times 3+6\times 0=4\times v_3+6\times v_{4}12=4v_3+6v_{4}2v_3+3v_4=6$

$2v_3+3v_4=6$----------------(1)

Here $e=1$

$e=\frac{velocityaftercollision}{velocitybeforecollision}$

$e=\frac{v_4-v_3}{3-0}=1v_4-v_3=3v_4=3+v_3$

Substitute above value in equation $\left(1\right)$

$2v_3+3(3+v_3)=6$

$2v_3+9+3v_3=6$

$5v_3+9=6$

$5v_3=-3$

$v_3=-0.6m/s$

$v_4=2.4m/s$

Hence, correct option is $\left(c\right)$option