A particle of mass 1 kg is moving on a circular path of radius 1 m. Its kinetic energy is K=bt4, where b= 1 J/s. The force acting on the particle at t = 1s is (2x)½N. The value of x is___________

A particle of mass 1 kg is moving on a circular path of radius 1 m. Its kinetic energy is K=bt4, where b= 1 J/s. The force acting on the particle at t = 1s is (2x)½N. The value of x is____________.

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answer is 0006.00.

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Detailed Solution

Here, 12mv2=bt4 or mv2=2bt4The centripetal force on the body is Fc=mv2R=2bt4R⇒v=2bmt2 and at=dvdt=2bmd(t)2dt=8bmt∴ Tangential force is Ft=mat=m8bmtThe force on the particle isF=2bt4R2+8mbt2=4+8=12=23N∴ 23=(2x)1/2⇒4×3=2x⇒x=6

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