Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Body P having mass M moving with speed u has head-on collision elastically with another body Q having mass m initially at rest. If $$m \ll M$$, body Q will have a maximum speed equal to 2u after collision.
Reason R: During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below:

In an elastic head-on collision between body P (mass $$M$$, speed $$u$$) and body Q (mass $$m$$, initially at rest), we apply conservation of momentum and conservation of kinetic energy.

Conservation of momentum gives: $$Mu = Mv_P + mv_Q$$, where $$v_P$$ and $$v_Q$$ are the velocities after collision.

Conservation of kinetic energy gives: $$\frac{1}{2}Mu^2 = \frac{1}{2}Mv_P^2 + \frac{1}{2}mv_Q^2$$.

Solving these two equations simultaneously, the velocity of body Q after collision is: $$v_Q = \frac{2M}{M + m} u$$.

When $$m \ll M$$, we have $$M + m \approx M$$, so: $$v_Q \approx \frac{2M}{M} u = 2u$$.

This confirms that body Q attains a maximum speed of $$2u$$, making Assertion A correct.

Reason R states that in an elastic collision, both momentum and kinetic energy are conserved. This is the very definition of an elastic collision and is certainly true. Furthermore, the formula $$v_Q = \frac{2M}{M+m}u$$ was derived directly from these two conservation laws, so R is indeed the correct explanation of A.

Hence the correct answer is Option 3: Both A and R are correct and R is the correct explanation of A.