Question

In an isolated system, (i.e. a system with no external force) total momentum of interacting particles is conserved. It follows

• A. Newton's first law
• B. Newton's second law
• C. Newton's third law
• D. Both (b) and (c)

Answer 1

Answer: (D)

Case I Consider two particles of a system having masses $m_1$ and $m_2$ are moving with velocities $v_1$ and $v_2$, respectively. Then, total linear momentum of the system
$p=m_1{v}_1+m_2{v}_2=p_1+p_2$
If $F$ is the external force acting on the system, then according to Newton's second law of motion,
$F=\frac{dp}{dt}$
For an isolated system, $F=0\Rightarrow \frac{dp}{dt}=0$
$\Rightarrow p=$ constant i.e. $p_1+p_2=$ constant
Case II Consider two particles of masses $m_1$ and $m_2$ moving along a straight line in opposite direction collide to each other, if $\Delta p_1$ and $\Delta p_2$ be the changes in momenta produced in time $\Delta t$, then according to the law of conservation of momentum, if no external force (for isolated system) is applied on the system
$\Rightarrow \Delta p_1+\Delta p_2=0$
$\Rightarrow \Delta p_2=-\Delta p_1$
$\Rightarrow \frac{\Delta p_2}{\Delta t}=-\frac{\Delta p_1}{\Delta t}$
$\Rightarrow$ Force on $m_2=-$ Force on $m_1$
$\left[\because F=\frac{dp}{dt}\right]$
$F_2=-F_1$
So, in an isolated system, when total momentum of interacting particles is conserved, it follow both, Newton's second and third laws.
Hence, options (b) and (c) are correct.