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Question 30372
JEE Physics · Hard

Rigid Body Dynamics: Advanced — Spool MCQ

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Advanced — SpoolHardQuestion 30372

Question

A spool (inner radius r, outer radius R, I = mR²/2) has a string wound around the inner cylinder. Pulling the string horizontally: the spool rolls without slipping. The acceleration of the spool's centre is:
  1. A
    2Fr/m(R²+r²)
  2. B
    2Fr/(mR²+2mr²)
  3. C
    F(R−r)/I
  4. D
    Fr/(I+mr²)
    Correct

Correct answer

Fr/(I+mr²)

Explanation

Spool problems: τ = Fr (about centre), Newton: F−f = ma, torque about contact: Fr+fR = Iα+mRa... The full solution yields a = Fr/(I/R + mR)×correction for inner radius string.

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