A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely…

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:
  1. T∝Rn/2
  2. T∝R3/2 for any n
  3. T∝Rn2+1
  4. T∝Rn+12

Solution

F=KRn⇒mV2r=KRn⇒V2∝KRn-1
⇒V∝1Rn-12⇒T=2πRV∝RV
⇒T∝R1Rn-12⇒T∝Rn+12

Asked in: JEE Main 2018 (08 Apr)

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