(A) For an object moving in a circular path with constant speed $v$ and radius $R$,the force $F$ acting on it is the centripetal force.$F = \frac{m v^

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(A) For an object moving in a circular path with constant speed $v$ and radius $R$,the force $F$ acting on it is the centripetal force.$F = \frac{m v^2}{R}$From this,we can express the term $m v^2$ as:$m v^2 = F R$The kinetic energy $(KE)$ of the object is given by the formula:$KE = \frac{1}{2} m v^2$Substituting the value of $m v^2$ from the force equation into the kinetic energy formula:$KE = \frac{1}{2} (F R)$Therefore,the kinetic energy is $\frac{1}{2} F R$.

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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An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of the object is ............

A
$\frac{1}{2} F R$
B
$F R$
C
$2 F R$
D
$\frac{1}{4} F R$

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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

$A$ string breaks if its tension exceeds $10 \, N$. $A$ stone of mass $250 \, g$ tied to this string of length $10 \, cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be .......... $rad/s$.

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An aircraft executes a horizontal loop at a speed of $720 \; km/h$ with its wings banked at $15^{\circ}$. What is the radius of the loop in $km$?

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$A$ 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:

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$A$ stone of mass $0.3\,kg$ attached to a $1.5\,m$ long string is whirled around in a horizontal circle at a speed of $6\,m s^{-1}$. The tension in the string is $............\,N$.

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$A$ car is moving on an overbridge of radius $R$ with a constant speed $v$. As the car is descending on the overbridge from point $B$ to $C$,the normal reaction on it due to the bridge:

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An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of the object is ............

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$A$ string breaks if its tension exceeds $10 \, N$. $A$ stone of mass $250 \, g$ tied to this string of length $10 \, cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be .......... $rad/s$.

An aircraft executes a horizontal loop at a speed of $720 \; km/h$ with its wings banked at $15^{\circ}$. What is the radius of the loop in $km$?

$A$ 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:

$A$ stone of mass $0.3\,kg$ attached to a $1.5\,m$ long string is whirled around in a horizontal circle at a speed of $6\,m s^{-1}$. The tension in the string is $............\,N$.

$A$ car is moving on an overbridge of radius $R$ with a constant speed $v$. As the car is descending on the overbridge from point $B$ to $C$,the normal reaction on it due to the bridge:

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