Question

Statement 1: If no external force acts on a system of particles, then the centre of mass will not move in any direction
Statement 2: If net external force is zero, then the linear momentum of the system remains constant.

• A. Statement 1 is false, Statement 2 is true
• B. Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1
• C. Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1
• D. Statement 1 is true, Statement 2 is false

Answer 1

The correct option is A Statement 1 is false, Statement 2 is true

$F_{external}=M{a}_{CM}$

Now , if net external force is zero then $a_{CM}=0$ i.e $v_f=v_i$.

Hence the centre of mass will move in the direction of initial state.

Also, $\frac{dP}{dt}=F_{external}=0$

Thus linear momentum $\left(P\right)$ is conserved.

Hence statement 1 is false and statement 2 is true