Question

In an elastic collision between two bodies. the physical quantity that is conserved is:

• A. kinetic energy
• B. momentum
• C. potential energy
• D. kinetic energy and momentum

Answer 1

Answer: (D)

A collision is said to be elastic if the total kinetic energy before and after collision remain the same or KE is conserved. Thus, if two bodies of masses $m_1$ and $m_2$ moving with velocities $u_1$ and $u_2$ collide in absence of external force also elastically and $v_1$ and $v_2$ are the final velocities, then according to conservation of momentum $m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$ Also, according to principle of conservation of KE $\frac{1}{2}m{u}_1^2+\frac{1}{2}m{u}_2^2=\frac{1}{2}m{v}_1^2+\frac{1}{2}m{v}_2^2$ Therefore, it is clear that both kinetic energy and momentum are conserved.