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NEET PHYSICSLAWS OF MOTIONMedium

Question

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance rr. The speed of the particle is:

A

Proportional to r2r^2

B

Independent of rr

C

Proportional to rr

D

Proportional to 1/r1/r

Step-by-Step Solution

  1. Identify Forces: For a particle moving in a circular orbit, the centripetal force required is provided by the given central attractive force.
  2. Centripetal Force Formula: The centripetal force acting on a particle of mass mm moving with speed vv in a circle of radius rr is Fc=mv2rF_c = \frac{mv^2}{r} [Source 61].
  3. Given Force Law: The problem states the attractive force FF is inversely proportional to distance rr. So, F1rF \propto \frac{1}{r} or F=krF = \frac{k}{r} where kk is a constant.
  4. Equate Forces: mv2r=kr\frac{mv^2}{r} = \frac{k}{r}
  5. Solve for Speed (vv): Multiplying both sides by rr eliminates it from the equation. mv2=kmv^2 = k v=kmv = \sqrt{\frac{k}{m}}
  6. Conclusion: Since kk and mm are constants, the speed vv is constant and independent of rr.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from LAWS OF MOTION. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSLAWS OF MOTIONparticlecircularactioncentralattractive

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