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Two objects of masses $100\, g$ and $200\, g$ are moving along the same line and direction with velocities of $2\, m\, s^{-1}$ and $1\, m\, s^{-1}$, respectively. They collide and after the collision, the first object moves at a velocity of $1.67\, m\, s^{-1}$. Determine the velocity(in $m/s$) of the second object.
$1.125$
$1.556$
$1.365$
$1.165$
Solution
Mass of one of the objects, $m_1 = 100 \,g = 0.1\, kg$
Mass of the other object, $m_2 = 200 \,g = 0.2 \,kg$
Velocity of $m_1$ before collision, $v_1 = 2\, m/s$
Velocity of $m_2$ before collision, $v_2 = 1\, m/s$
Velocity of $m_1$ after collision, $v_3 = 1.67 \,m/s$
Velocity of $m_2$ after collision $= v_4$
According to the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
$m_1v_1 + m_2v_2 = m_1v_3 + m_2v_4$
$0.1\times 2 + 0.2\times 1 = 0.1\times 1.67 + 0.2\times v_4$
$0.4 = 0.67 + 0.2\times v_4$
$v_4 = 1.165\, m/s$
Hence, the velocity of the second object becomes $1.165\, m/s$ after the collision.
