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Question

(B) The angular velocity $\omega$ of a particle moving with velocity $v$ at a distance $r_{\perp}$ from a point is given by $\omega = \frac{v_{\perp}}

Vedclass · Accepted Answer

$1:2$

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(B) The angular velocity $\omega$ of a particle moving with velocity $v$ at a distance $r_{\perp}$ from a point is given by $\omega = \frac{v_{\perp}}{r_{\perp}}$,where $v_{\perp}$ is the component of velocity perpendicular to the position vector.At point $B$,the velocity $v$ is perpendicular to the diameter $AB$.For point $A$,the distance is $AB = 2a$. Thus,the angular velocity about $A$ is $\omega_A = \frac{v}{2a}$.For point $C$,the distance is $CB = a$. Thus,the angular velocity about $C$ is $\omega_C = \frac{v}{a}$.The ratio of angular velocities is $\frac{\omega_A}{\omega_C} = \frac{v/2a}{v/a} = \frac{1}{2}$.

$A$ 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:

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