Question

A particle is moving in a circle of radius $r$ with a uniform speed $u$. $C$ is the centre of the circle and $AB$ is the diameter. The angular velocity of $P$ about $A$ and $C$ are in the ratio :

• A. $1:2$
• B. $2:1$
• C. $1:3$
• D. $3:1$

Answer 1

The correct option is A $1:2$


Let,
$\angle PCB=\varphi$
$\angle PAB=\theta$

So,
$2\theta =\varphi$
$\Rightarrow 2\frac{d\theta }{dt}=\frac{d\varphi }{dt}$

$\Rightarrow 2{\omega }_A={\omega }_C$

$\Rightarrow {\omega }_A:{\omega }_C=1:2$