﻿ Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision?  from Physics Work, Energy and Power Class 11 Manipur Board

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Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision?

The total momentum before and after a collision in each case is constant.

For an elastic collision,

Total kinetic energy of a system remains conserved before and after the collision.

For mass of each ball bearing m, we can write,

Total kinetic energy of the system before collision,

= mV2 +(2m) × 02
=mV2

Case (i)

Total kinetic energy of the system after collision,

=  m × 0 + (2m) ()2
= mV2
Hence, the kinetic energy of the system is not conserved in case (i).

Case (ii)

Total kinetic energy of the system after collision,

=x(2m) × 0 + mV2
=  mV2
Hence, the kinetic energy of the system is conserved in case (ii).

Case (iii)

Total kinetic energy of the system after collision,

= ()(3m)()2
= ()mV

Hence, the kinetic energy of the system is not conserved in case (iii).

Hence, Case II is the only possibility.
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