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(B) Let the particle $P$ be at position $B$ at a given instant. The speed of the particle is $u$.The angular velocity of $P$ about the centre $C$ is g

Vedclass · Accepted Answer

$1 : 2$

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(B) Let the particle $P$ be at position $B$ at a given instant. The speed of the particle is $u$.The angular velocity of $P$ about the centre $C$ is given by $\omega_C = \frac{u}{r} = \frac{u}{a}$.The angular velocity of $P$ about point $A$ is given by $\omega_A = \frac{v_{\perp}}{r_{AP}}$,where $v_{\perp}$ is the component of velocity perpendicular to the line $AP$. At point $B$,the velocity $u$ is perpendicular to the diameter $AB$. The distance $AP = 2a$.Thus,$\omega_A = \frac{u}{2a}$.Taking the ratio of angular velocities:$\frac{\omega_A}{\omega_C} = \frac{u/2a}{u/a} = \frac{1}{2}$.Therefore,the ratio is $1 : 2$.

$A$ particle $P$ is moving in a circle of radius $a$ 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:

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