(C) Let the angular velocity be $\Omega = 2\omega$. For particle $B$ of mass $m$ at distance $2r$ from $O$,the tension $T_{AB}$ provides the necessary

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(C) Let the angular velocity be $\Omega = 2\omega$. For particle $B$ of mass $m$ at distance $2r$ from $O$,the tension $T_{AB}$ provides the necessary centripetal force: $T_{AB} = m \Omega^2 (2r) = m (2\omega)^2 (2r) = m (4\omega^2) (2r) = 8m\omega^2 r$. For particle $A$ of mass $2m$ at distance $r$ from $O$,the net force towards the center is $T_{OA} - T_{AB}$: $T_{OA} - T_{AB} = (2m) \Omega^2 r = (2m) (2\omega)^2 r = (2m) (4\omega^2) r = 8m\omega^2 r$. Substituting $T_{AB} = 8m\omega^2 r$: $T_{OA} = 8m\omega^2 r + 8m\omega^2 r = 16m\omega^2 r$. Therefore,the ratio is: $T_{OA} / T_{AB} = (16m\omega^2 r) / (8m\omega^2 r) = 2 / 1 = 2 : 1$.

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

Medium

Two particles of mass $2m$ and $m$ are attached to a light string as shown. The complete system is rotated in a horizontal circle with a constant angular velocity $2\omega$ about an axis passing through point $O$ and perpendicular to the plane of the circle. Find the ratio $T_{OA} / T_{AB}$,where $T_{OA}$ and $T_{AB}$ are the tensions in strings $OA$ and $AB$ respectively.

A
$4 : 1$
B
$1 : 1$
C
$2 : 1$
D
$1 : 2$

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2 Motion in a Plane

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

$A$ particle starts from rest and performs circular motion of constant radius with speed given by $v = \alpha \sqrt{x}$,where $\alpha$ is a constant and $x$ is the distance covered. The correct graph of the magnitude of its tangential acceleration $(a_t)$ and centripetal acceleration $(a_c)$ versus $t$ will be:

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$A$ particle is moving with constant speed along a uniform helical path $(a)$ and a spiral path $(b)$ separately,as shown in the figure.

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$A$ particle is released on a vertical smooth semicircular track from point $X$ so that $OX$ makes an angle $\theta$ from the vertical (see figure). The normal reaction of the track on the particle vanishes at point $Y$ where $OY$ makes an angle $\phi$ with the horizontal. Then

DifficultJEE MAIN 2014

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$A$ particle of mass $m$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r = \frac{L}{\sqrt{2}}$. The speed of the particle will be:

DifficultJEE MAIN 2021

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$A$ body of mass $m$ is moving with speed $V$ along a circular path of radius $r$. Now,the speed is reduced to $\frac{V}{2}$ and the radius is increased to $3r$. For this change,the initial centripetal force needs to be:

MediumMHT CET 2021

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$A$ particle is moving with constant speed along a uniform helical path $(a)$ and a spiral path $(b)$ separately,as shown in the figure.

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