(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 3-2.Motion in 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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3-2.Motion in Plane

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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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$A$ particle rotates in a horizontal circle of radius $R$ in a conical funnel with constant speed $V$. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is (where $g$ is the acceleration due to gravity):

Consider the following statements:Assertion $(A)$: $A$ cyclist always bends inwards while negotiating a curve.Reason $(R)$: By bending,he provides the necessary centripetal force by shifting his centre of gravity.

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is

Three particles of equal mass are tied to a string and rotated in a horizontal plane as shown. What is the ratio of tensions in the three parts of the string?

If a stone of mass $0.5 \ kg$ tied to one end of a wire is whirled in a circular path of radius $2 \ m$ with a speed $40 \ rev/min$ in a horizontal plane,then the tension in the wire is nearly (in $N$)

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Consider the following statements:
Assertion $(A)$: $A$ cyclist always bends inwards while negotiating a curve.
Reason $(R)$: By bending,he provides the necessary centripetal force by shifting his centre of gravity.