Question

The velocity of the centre of mass of a system changes from $\overrightarrow{v_1}=4\hat{i}\text{m/s}$ to $\overrightarrow{v_2}=3\hat{j}\text{m/s}$ during time $\Delta t=2\text{s}$. If the mass of the system is $m=10\text{kg}$, the magnitude of constant force acting on the system is

• A. $25\text{N}$
• B. $20\text{N}$
• C. $50\text{N}$
• D. $5\text{N}$

Answer 1

The correct option is A $25\text{N}$

The force is given by relation,
$\overrightarrow{F}=m\frac{\Delta {\overrightarrow{v}}_{cm}}{\Delta t}=\frac{10(3\hat{j}-4\hat{i})}{2}=5(3\hat{j}-4\hat{i})=15\hat{j}-20\hat{i}$
$|\overrightarrow{F}|=\sqrt{{15}^2+(-20{)}^2}=25\text{N}$