Question

A stone of mass m tied to a spring of length l is rotating along a circular path with constant speed v. The torque on the stone is ______.

Options

• mv²l

• zero

• mlv

• `(mv^2)/l`

Answer 1

A stone of mass m tied to a spring of length l is rotating along a circular path with constant speed v. The torque on the stone is zero.

Explanation:

Torque depends on the force and its perpendicular distance from the axis.

Here, the stone is moving in a circle, so the force acting on it is the centripetal force provided by the spring:

F = `(mv^2)/l`

This force always acts along the radius (towards the centre), i.e., along the same direction as the position vector `vecr`.

`vecτ = vecr xx vecF`

Since `vecr and vecF`are in the same direction, the angle between them is 0°.

τ = r F sin 0°

= 0

So, even though the stone is rotating, the torque about the centre is zero because the force is purely radial.