Question

A body of mass 2 kg moving with a velocity 3 m/s collides with a body of mass 1 kg moving with a velocity of 4 m/s in opposite direction. If the collision is head on an completely inelastic, then :

• A. both particles move together with velocity (2/3) m/s
• B. the momentum of system is 2 kg m/s throughtout
• C. the momentum of system is 10 kg m/s
• D. the loss of KE of system is (49/3) J

Answer 1

Answer: (A), (B), (D)

The correct options are
A both particles move together with velocity (2/3) m/s
B the momentum of system is 2 kg m/s throughtout
D the loss of KE of system is (49/3) J

Given : $m_1=2kg$ $m_2=1kg$ $u_1=3$ $m/s$ $u_2=4$ $m/s$

Let the common velocity of the combined body be $V$

Mass of combined body $M=2+1=3kg$

Applying conservation of momentum :

$2\times 3-1\times 4=3\times V$ $⟹V=\frac{2}{3}$ $m/s$

Momentum of the system $P=2\times 3-1\times 4=2$ kg m/s

Loss in kinetic energy of the system due to collision $\Delta K.E=K.E_i-K.E_f$

$\Delta K.E=\frac{1}{2}\left(2\right)\times 3^2+\frac{1}{2}\left(1\right)\times 4^2-\frac{1}{2}\left(3\right)\times (\frac{2}{3}{)}^2$

$⟹\Delta K.E=\frac{49}{3}$ J