Question

A system consists of two small spheres of mass $1\text{kg}$ and $2\text{kg}$ interconnected by a weightless spring. At $t=0$, the spheres are set in motion with initial velocities as shown in the figure. The position vector of centre of mass at $t=0$ is $\left(20\hat{j}\right)\text{m}$. Initially, spring is in its natural length. The system moves in earth's gravitational field. The momentum of the system at $t=2\text{s}$ in $\text{kg-m/s}$ is

$[g=10{\text{m/s}}^2,\text{com is initial centre of mass}]$

• A. $12\hat{i}-32\hat{j}$
• B. $16\hat{i}-64\hat{j}$
• C. $18\hat{i}-64\hat{j}$
• D. $12\hat{i}-18\hat{j}$

Answer 1

The correct option is C $18\hat{i}-64\hat{j}$

Momentum of system at $t=0$ is,

$\overrightarrow{p_i}=1(8\hat{i}+6\hat{j})+2(5\hat{i}-5\hat{j})=18\hat{i}-4\hat{j}$

Momentum of system at $t=2\text{s}$ is,

${\overrightarrow{p}}_f={\overrightarrow{F}}_{\text{ext}}.\Delta t+\overrightarrow{p_i}=-60\hat{j}+(18\hat{i}-4\hat{j})=18\hat{i}-64\hat{j}$

Hence, option $\left(C\right)$ is the correct answer.