Question

Assertion :No external force acts on a system of two spheres which undergo a perfectly elastic head-on collision. The minimum kinetic energy of this system is zero if the net momentum of the system is zero. Reason: If any two bodies undergo a perfectly elastic head-on collision, at the instant of maximum deformation, the complete kinetic energy of the system is converted to deformation potential energy of the system.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

If any two bodies undergo a perfectly elastic head-on collision, at the instant of maximum deformation, the two bodies are moving with same velocity. So if the velocity is zero that means that KE at this instant is zero and and the total initial energy is converted into potential energy. But this is not always the case it is possible that the there is some KE in the system when there is maximum deformation. This proves that the reason is wrong.
Assertion is correct, since the net momentum of the system is zero, the velocity of both the particles at maximum deformation will be given by $m_1{v}_1+m_2{v}_2=(m_1+m_2)V=0\Rightarrow V=0\Rightarrow KE=0$