(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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$A$ train is moving with a speed of $12 \,m/s$ on rails which are $1.5 \,m$ apart. To negotiate a curve of radius $400 \,m$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10 \,m/s^2$): (in $\,cm$)

$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. Then the force exerted by the liquid at the other end is

With what frequency should a particle of mass $m$ be rotated so that a body of mass $M$ remains stationary?

$A$ body of mass $M = 100 \; g$ is rotating with an angular frequency of $2/\pi \; \text{rev/sec}$ as shown in the figure. What is the angle made by the string with the vertical? $(g = 10 \; m/s^2)$

$A$ coin placed on a rotating turntable just slips if it is placed at a distance of $4 \ cm$ from the centre. If the angular velocity of the turntable is doubled,it will just slip at a distance of: (in $cm$)

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