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NEET PHYSICSLAWS OF MOTIONMedium

Question

A gramophone record is revolving with an angular velocity ω\omega. A coin is placed at a distance rr from the centre of the record. The static coefficient of friction is μ\mu. The coin will revolve with the record if:

A

r=μgω2r = \frac{\mu g}{\omega^2}

B

r<ω2μgr < \frac{\omega^2}{\mu g}

C

rμgω2r \le \frac{\mu g}{\omega^2}

D

rμgω2r \ge \frac{\mu g}{\omega^2}

Step-by-Step Solution

  1. Identify Forces: For the coin to revolve with the record without slipping, it requires a centripetal force directed towards the centre. The only force capable of providing this in the horizontal plane is the static friction (fsf_s) between the coin and the record.
  2. Centripetal Force: The required centripetal force is Fc=mrω2F_c = mr\omega^2, where mm is the mass of the coin.
  3. Friction Limit: The maximum value of static friction is limiting friction, fs,max=μNf_{s,max} = \mu N. Since the coin is on a horizontal surface, the normal reaction N=mgN = mg. Thus, fs,max=μmgf_{s,max} = \mu mg.
  4. Condition for No Slipping: The coin will revolve with the record only if the required centripetal force is less than or equal to the maximum available static friction. Fcfs,maxF_c \le f_{s,max} mrω2μmgmr\omega^2 \le \mu mg Canceling mass mm (since m>0m > 0): rω2μgr\omega^2 \le \mu g rμgω2r \le \frac{\mu g}{\omega^2} (Reference: NCERT Class 11, Physics Part I, Chapter 5, Section 5.10, Motion of a car on a level road).

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 MOTIONgramophonerecordrevolvingangularvelocity

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