(B) The sphere $B$ of mass $2M$ is rotating in a circle of radius $d$ about the pivot $A$ with a period $P$. The angular velocity $\omega$ is given by

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(B) The sphere $B$ of mass $2M$ is rotating in a circle of radius $d$ about the pivot $A$ with a period $P$. The angular velocity $\omega$ is given by $\omega = \frac{2\pi}{P}$. The centripetal force required for the circular motion of sphere $B$ is provided by the tension $T$ in the rod. Thus,$T = (2M) \cdot d \cdot \omega^2$. Substituting the value of $\omega$: $T = 2M \cdot d \cdot \left(\frac{2\pi}{P}\right)^2$ $T = 2M \cdot d \cdot \frac{4{\pi}^2}{P^2}$ $T = \frac{8{\pi}^2Md}{P^2}$.

Class 11 Physics 2 Motion in a Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ dumbbell is placed on a frictionless horizontal table. Sphere $A$ is attached to a frictionless pivot so that $B$ can be made to rotate about $A$ with constant angular velocity. If $B$ (mass $2M$) makes one revolution in period $P$,the tension in the rod (length $d$) is

A
$\frac{4{\pi}^2Md}{P^2}$
B
$\frac{8{\pi}^2Md}{P^2}$
C
$\frac{4{\pi}^2Md}{P}$
D
$\frac{2Md}{P}$

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Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ dumbbell is placed on a frictionless horizontal table. Sphere $A$ is attached to a frictionless pivot so that $B$ can be made to rotate about $A$ with constant angular velocity. If $B$ (mass $2M$) makes one revolution in period $P$,the tension in the rod (length $d$) is

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