Q. Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement II Principle of conservation of momentum holds true for all kinds of collisions.
A) Statement I is true, statement II is true, statement II is the correct explanation of statement I.
B) Statement I is true Statement II is true, Statement II is not correct explanation of statement I.
C) Statement I is false, Statement II is true.
D) Statement I is true, Statement II is false.
Explanation
(d) If it is a completely inelastic collision then
$m_{1}v_{1} + m_{2}v_{2} = m_{1}v + m_{2}v$
$\ v = \frac{m_{1}v_{1} + m_{2}v_{2}}{m_{1} + m_{2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underset{\mathbf{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v}_{\mathbf{1}}}{\overset{\mathbf{m}_{\mathbf{1}}\mathbf{\ \ \ \ \ \ \ \ \ }}{\rightarrow}}\underset{\mathbf{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v}_{\mathbf{2}}}{\overset{\mathbf{m}_{\mathbf{2}}\mathbf{\ \ \ \ \ \ \ \ \ }}{\rightarrow}}$
$KE = \frac{p_{1}^{2}}{2m_{1}} + \frac{p_{2}^{2}}{2m_{2}}$
As $p_{1}\ and\ p_{2}$ both simultaneously cannot be zero therefore total KE cannot lost.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.