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Standard XII

Physics

The Principle

A mass rotati...

Question

A mass rotating freely in a horizontal circle of radius 1 on a friction less smooth table supports a stationary mass 2m, attached to the other end of the string passing through smooth hole O in stable, hanging vertically. Find the angular velocity of rotation.

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Solution

If mass m is rotating with angular velocity w than a centrifugal force acting in the mass m which balance the tension which is exerted by the mass 2m is $2 m g$
centrifugal force = tension in the rope
$\Rightarrow m w^{2} r = 2 m g$
where r equal to 1m
$\Rightarrow w = \sqrt{\frac{2 g}{r}}$
Hence the angular velocity w is $\sqrt{\frac{2 g}{r}}$

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A mass rotating freely in a horizontal circle of radius 1 on a friction less smooth table supports a stationary mass 2m, attached to the other end of the string passing through smooth hole O in stable, hanging vertically. Find the angular velocity of rotation.

If mass m is rotating with angular velocity w than a centrifugal force acting in the mass m which balance the tension which is exerted by the mass 2m is 2mgcentrifugal force = tension in the rope⇒mw2r=2mgwhere r equal to 1m⇒w=√2grHence the angular velocity w is √2gr