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 $C$ 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 $\frac{{\omega }_A}{{\omega }_C}=\frac{v/2r}{v/r}=\frac{1}{2}$