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 pf−pi=(−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.Ef−K.Ei=0
Hence, momentum changes by 2mv in magnitude but kinetic energy remains same.