Question

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

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

Answer 1

Answer: (B)

From properties of $\Delta$
If $\angle CAP=\theta$
then $\angle BCP=2 \, \theta$
$\omega _{A} = \frac{d \theta }{d t}$
$\omega _{C} = 2 \frac{d \theta }{d t}$
$\omega _{A} : \omega _{C} = 1 : 2$