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A pendulum of mass m and length l is released from rest in a h

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A pendulum of mass m and length l is released from rest in a horizontal position.A naill at a distance d below the pivot,causes the mass to move along the path indicated by the dotted line.The minimum distance such that the mass will swing completely round in the circle shown.

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A pendulum of mass m and length l is released from rest in a horizontal position.A naill at a distance d below the pivot,causes the mass to move along the path indicated by the dotted line.The minimum distance such that the mass will swing completely round in the circle shown.

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Text solutionVerified

Let

m

be a point mass. The velocity at the instant when the pendulum strikes the nail is

v = 2 g l

The angular momentum of the mass w.r.t the point at whih the nail locates is considered during the collision.

Then the velocity of the mass at this instant be

v_{1}

and have

\frac{m v _{1}^{2}}{l - d} = m g

v

=> v_{1}^{2} = (l - d) g

From the energy equation,

\frac{m v ^{2}}{2} = \frac{m v _{1}^{2}}{2} + 2 m g (l - d) g

=> 2 g l = (l - d) g + 4 (l - d) g

d = \frac{3 l}{5}

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Question Text	A pendulum of mass m and length l is released from rest in a horizontal position.A naill at a distance d below the pivot,causes the mass to move along the path indicated by the dotted line.The minimum distance such that the mass will swing completely round in the circle shown.
Answer Type	Text solution:1
Upvotes	150

A pendulum of mass m and length l is released from rest in a horizontal position.A naill at a distance d below the pivot,causes the mass to move along the path indicated by the dotted line.The minimum distance such that the mass will swing completely round in the circle shown.

Text solutionVerified

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