Question

A particle P is moving in a circle of radius 'a' with a uniform speed v . C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and B are in the ratio

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 4 : 1

Answer 1

The correct option is B 1 : 2

Angular velocity of particle P about point A,
${\omega }_A$ = $\frac{v}{r_{AB}}$ = $\frac{v}{2r}$
Angular velocity of particle P about point C,
${\omega }_C$ = $\frac{v}{r_{BC}}$ = $\frac{v}{r}$
Ratio $\frac{{\omega }_A}{{\omega }_C}$ = $\frac{\frac{v}{2r}}{\frac{v}{r}}$ = $\frac{1}{2}$