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Question

A particle of mass m is moving in a circle with uniform speed v. In moving from a point to another diametrically opposite point,

A
the momentum changes by mv
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B
the momentum changes by 2mv
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C
the kinetic energy changes by (12)mv2
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D
the kinetic energy changes by mv2
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Solution

The correct option is B the momentum changes by 2mv
Let the particle of mass m be moving in anticlockwise sense and A and B are the diametrically opposite points as shown in the figure.


Now we have
initial momentum of the particle at A is pi=mv^j
and final momentum of the particle at B is pf=mv^j
So, change in momentum is pfpi=(mv^j)(mv^j)=2mv^j

Also, we have
Initial kinetic energy K.Ei=12mv2
Final kinetic energy K.Ef=12mv2
So, change in kinetic energy is K.EfK.Ei=0

Hence, momentum changes by 2mv in magnitude but kinetic energy remains same.

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