Question

Two particles revolve concentrically in a horizontal plane in the same direction. The time required to complete one revolution for particle $A$ is $3min$, while for particle $B$ is $1min$. The time required for $A$ to complete one revolution relative to $B$ is

• A. $2min$
• B. $1min$
• C. $1.5min$
• D. $1.25min$

Answer 1

The correct option is C $1.5min$

Let both moves in a circle of radius r.

For A: $T_A=3min$

Thus $v_A=\frac{2\pi r}{3}$

For B: $T_B=1min$

$v_B=\frac{2\pi r}{1}$

Time require to complete one revolution for A relative to B, $T=\frac{2\pi r}{v_B-v_A}$

$T=\frac{2\pi r}{\frac{2\pi r}{1}-\frac{2\pi r}{3}}$

$⟹T=1.5min$