Q. 37

# The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.13. If the length of the pendulum is 1m, calculate(a) the height to which bob A will rise after collision.(b) the speed with which bob B starts moving. Neglect the size of the bobs and assume the collision to be elastic.

Let be the mass of the bob and be the initial height of the bob.

Potential energy of a particle raised to the height h is =

And kinetic energy of the particle with velocity v is given as

=

Just before collision, bob A reaches ground and its potential energy gets converted to kinetic energy,

conserving energy we get,

-----(1)

(a) Using the result that when two bodies of same mass collide, their velocities are mutually interchanged,

Bob A must come to rest and bob B must gain the velocity in equation (1).

a) from above we conclude the bob A will not rise to any height since its velocity will become zero after collision.

b) the velocities are interchanged,

velocity of bob B =

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