A body of mass m is moving in a circle of rad | vedclass

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(B) The force acting on the body is the centripetal force,which is always directed towards the center of the circular path.The displacement of the bod

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(B) The force acting on the body is the centripetal force,which is always directed towards the center of the circular path.The displacement of the body at any instant is along the tangent to the circle at that point.Since the radius (and thus the centripetal force) is always perpendicular to the tangent (displacement),the angle $	heta$ between the force vector $\vec{F}$ and the displacement vector $d\vec{s}$ is always $90^{\circ}$.The work done $W$ is given by the dot product of force and displacement: $W = \int \vec{F} \cdot d\vec{s} = \int F \cos(90^{\circ}) ds$.Since $\cos(90^{\circ}) = 0$,the work done by the centripetal force is always zero,regardless of the distance traveled along the circumference.

$A$ body of mass $m$ is moving in a circle of radius $r$ with a constant speed $u$. The force on the body is $mv^2/r$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

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