Question

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

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

Answer 1

The correct option is C 1.5 min

Angular velocity of A w.r.t B, ${\omega }_{AB}=|{\omega }_A-{\omega }_B|$

We know that $\omega =\frac{2\pi }{T}$

$\Rightarrow \frac{2\pi }{T_{AB}}=|\frac{2\pi }{T_A}-\frac{2\pi }{T_B}|$
where $T_{AB}$ is time taken by A w.r.t particle B.

$\Rightarrow T_{AB}=\left|\frac{T_A{T}_B}{T_A-T_B}\right|=\frac{3\times 1}{3-1}=\frac{3}{2}=1.5\text{min}$

$\therefore T_{AB}=1.5\text{min}$