Question

Statement-1: Uniform relative velocity does not imply that the observer is moving with uniform velocity.
Statement-2: If two particles are projected simultaneously then velocity of one projectile w.r.t. other is uniform.

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

Answer 1

The correct option is B Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for statement-1.

Let $A$ and $B$ be the two particles projected at an angle $\alpha$ and $\beta$ respectively.
Let $v_1$ and $v_2$ be the initial velocities of $A$ and $B$ respectively.
At time $t$, velocity of $A$ and $B$ can be given by
${\overrightarrow{v}}_A=v_1\cos \alpha \hat{i}+(v_1\sin \alpha -gt)\hat{j}$
and ${\overrightarrow{v}}_B=v_2\cos \beta \hat{i}+(v_2\sin \beta -gt)\hat{j}$
$\therefore {\overrightarrow{v}}_{AB}=(v_1\cos \alpha -v_2\cos \beta )\hat{i}+(v_1\sin \alpha -v_2\sin \beta )\hat{j}$
${\overrightarrow{v}}_{AB}=$ constant but ${\overrightarrow{v}}_B$ is not uniform (here $B$ is the observer)
So relative velocity is uniform even if observer may not have uniform motion.
So, statement-1 and statement-2 both are correct but statement-2 is not the correct explanation of statement-1.