A body of mass m is moving with a constant speed v in a circle of radius r . Find the work done by the centripetal force in moving the body over half the circumference of the circle.

Question

A body of mass m is moving with a constant speed v in a circle of radius r . Find the work done by the centripetal force in moving the body over half the circumference of the circle. (A) (m v2/π r2) (B) zero (C) (m v2/r2) (D) (π r2/m v2)

Tardigrade Admin · Accepted Answer

In uniform circular motion speed and kinetic energy remains constant, work done is independent on path.
Here the centripetal force and instantaneous displacement are perpendicular to each other

W = F \to \cdot s \to = F scos θ^{\circ} (θ = 9 0^{\circ}) = 0

therefore the work done by centripetal force is is zero.

Q. A body of mass $m$ is moving with a constant speed $v$ in a circle of radius $r$ . Find the work done by the centripetal force in moving the body over half the circumference of the circle.

$\frac{m v ^{2}}{π r ^{2}}$

zero

$\frac{m v ^{2}}{r ^{2}}$

$\frac{π r ^{2}}{m v ^{2}}$

Q. A body of mass m is moving with a constant speed v in a circle of radius r . Find the work done by the centripetal force in moving the body over half the circumference of the circle.

πr2mv2​

zero

r2mv2​

mv2πr2​

In uniform circular motion speed and kinetic energy remains constant, work done is independent on path. Here the centripetal force and instantaneous displacement are perpendicular to each other W=F→⋅s→=Fscosθ∘(θ=90∘)=0 therefore the work done by centripetal force is is zero.

Q. A body of mass $m$ is moving with a constant speed $v$ in a circle of radius $r$ . Find the work done by the centripetal force in moving the body over half the circumference of the circle.

$\frac{m v ^{2}}{π r ^{2}}$

$\frac{m v ^{2}}{r ^{2}}$

$\frac{π r ^{2}}{m v ^{2}}$