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Machine Design
Design Against Static Load
GATE 2012
Hard

A force of 400 N is applied directly (no lever arm) to one end of the band in a band-brake system wrapped around a drum of 0.5 m diameter, with the other end of the band anchored to a fixed support; the wrapping angle is 180°. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied, in N.m is

  • A100.6
  • 54.4
  • C22.1
  • D15.7

Explanation

Since the 400 N force is applied directly (no lever), it equals the tight-side tension T1=400 N. Using the belt-friction ratio T1/T2=e^(μθ) with θ=π rad: e^(0.25π)=e^0.7854≈2.193. T2=400/2.193≈182.4 N. Braking torque=(T1−T2)×r=(400−182.4)×0.25≈54.4 N.m.

Source: GATE ME 2012 (Booklet Code A) (2012)

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