Question

Two particles revolve concentrically in a horizontal place in the same direction. The time required to complete one revolution for particle A is 3 min, while for particle B 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 speed of a revolving object is given as

$\omega =\frac{2\pi }{T}$

Now the angular speed of A is given by

${\omega }_a=\frac{2\pi }{3}$

angular speed of B is given by

${\omega }_b=\frac{2\pi }{1}$

now the relative angular speed of B with respected to A

${\omega }_{ba}={\omega }_b-{\omega }_a$

${\omega }_{ba}=\frac{2\pi }{1}-\frac{2\pi }{3}$

so the time to compete one revolution is given as

$\frac{2\pi }{{\omega }_{ba}}$

$\frac{1}{T}=1-\frac{1}{3}$

$T=1.2min$