Two solid rubber balls, A and B having masses $200g$ and $400g$ respectively are moving in opposite directions with velocity of A equal to $0.3\,m{s^{ - 1}}$. After collision the two balls come to rest, then the velocity of B is-
A. $0.15\,m{s^{ - 1}}$
B. $1.5\,m{s^{ - 1}}$
C. $ - 0.15\,m{s^{ - 1}}$
D. None of the above

Hint:In order to solve this question, we will apply the law of conservation of momentum and then using this principle and equations we will determine the velocity of ball B before the collision.

Formula used:
The principle of conservation of linear momentum says that Initial momentum of a system is always equal to final momentum of a system. ${P_i} = {P_f}$ where $P = mv$ denotes the momentum of a body defined as the product of mass of the body and the velocity of the body.

Complete step by step solution:
According to the question, we have given that mass of body A and B are ${m_A} = 200g = 0.2kg$ and ${m_B} = 400g = 0.4kg$ and initial velocity of body A was ${u_A} = 0.3m{s^{ - 1}}$ and let initial velocity of B was ${u_B}$ so total initial momentum of the system was;
${P_i} = {m_A}{u_A} + {m_B}{u_B} \\
\Rightarrow {P_i} = 0.2(0.3) + 0.4({u_B}) \to (i) \\ $
After collision, both bodies came to rest which means final velocities of both bodies is zero so final momentum will be zero ${P_f} = 0 \to (ii)$ So, using principle of conservation of linear momentum we have,
${P_i} = {P_f}$
So using equations (i) and (ii) we get,
$0.06 + 0.4\,{u_B} = 0 \\
\Rightarrow {u_B} = \dfrac{{ - 0.06}}{{0.4}} \\
\therefore {u_B} = - 0.15\,m{s^{ - 1}} \\ $
Hence, the correct answer is option C.

Note: Other than the law of conservation of linear momentum, the other two most significant conservation laws are the law of conservation of energy, which states that the system's energy is preserved, and the law of conservation of angular momentum in rotational dynamics.