Question

A body moves along a circular path of radius 5m.the coefficient of friction between the surface of the path and the body is 0.5.the angular velocity in rad/s with which the body should move so that it does not leave the path is

Answer 1

Answer:

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Answer 2

Given that,

Radius of the circular path, r = 5 m

The coefficient of friction between the surface of the path and the body is 0.5

To find,

The angular velocity with which the body should move so that it does not leave the path is.

Solution,

When the object moves in circular path, the centripetal fore acts on it. The frictional force is balanced by the centripetal force. So,

$\mu mg=m\omega^2r$

$\omega$ is angular velocity

$\omega=\sqrt{\dfrac{\mu g}{r}} \\\\\omega=\sqrt{\dfrac{0.5\times 10}{5}} \\\\\omega=1\ rad/s$

So, the angular velocity in  with which the body should move so that it does not leave the path is 1 rad/s.

Learn more,

Centripetal force

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