Question

A particle $\left(P\right)$ is moving in a circle of radius $\left(a\right)$ with a uniform speed $\left(v\right)$. $c$ is the center of the circle and $AB$ is a diameter. The angular velocity of particle when it is at point $B$ about $\left(A\right)$ and $\left(C\right)$ are in the ratio$:$

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

Answer 1

The correct option is B $1:2$

The angular velocity of a particle about any point is given by:

$\omega =v/r$ ,

where, $v=$ speed of particle

$r=$ distance of particle from point

Here, given speed of particle is constant.

Angular speed about point A, ${\omega }_A=v/AB=v/2a$ ( because $AB=2a$)

Angular speed about centre C, ${\omega }_A=v/BC=v/a$ ( because $BC=a$)

Therefore, $\frac{{\omega }_A}{{\omega }_C}=\frac{1}{2}$