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

Answer: (B)

1 : 2

Answer 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 $\frac{\omega_{A}}{\omega_{C}} = \frac{v ⥂ / ⥂ 2r}{v ⥂ / ⥂ r} = \frac{1}{2}.$