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Q.

A particle moving with kinetic energy 3J makes an elastic collision (head on )with a stationary particle which has twice its mass, During impact:

 

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a

The minimum kinetic energy  of the system is 1J

b

Momentum and total energy are conserved at energy instant

c

The ratio of kinetic energy to potential energy of the system first decreases and then increases

d

The maximum elastic potential energy of the systems is 2J

answer is A, B, C, D.

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Detailed Solution

In a head on elastic collision between two particles , the kinetic energy becomes minimum and potential energy becomes maximum at the instant when they move with a common velocity. The momentum and energy are conserved at energy instant. 12mu2 = 3Jmu = (m +2m) v =v =u3

Minimum kinetic energy of the system 12(3m)u32 = 1J

Maximum elastic  potential energy of system = (3-1)J = 2J

During the course of collision ,due to deformation elastic potential energy of the system first increases and kinetic energy decreases , after maximum deformation the objects gradually regain their shapes and as a result elastic potential energy decreases and kinetic energy increases.

 

 

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