Two objects of masses $100\ g$ and, $200\ g$ are moving along the same line and direction with velocities of $2\ m/s$ and $1\ m/s$ respectively. They collide and after the collision, the first object moves at a velocity $1.67\ m/s$. Determine the velocity of the second object.

Mass of the first object $m_1=100\ g=\frac{100}{1000}\ kg.=0.1\ kg.$

Mass of the second object $m_2=200\ g=\frac{200}{1000}\ kg.=0.2\ kg.$

Velocity of the first object $u_1=2\ m/s$

Velocity of the second object $u_2=1\ m/s$

Velocity of the first object after collision $v_1=1.67\ m/s$

Let $v_2$ be the velocity of the second object.

According to the law of conservation of momentum,

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Or $0.1\times2+0.2\times1=0.1\times1.67+0.2\times v_2$

Or $0.2+0.2=0.167+0.2v_2$

Or $0.4=0.167+0.2v_2$

Or $0.2v_2=0.4-0.167$

Or $v_2=\frac{0.233}{0.2}$

Or $v_2=1.165\ m/s$

Therefore, the velocity of the second object after the collision.

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Updated on: 10-Oct-2022

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