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AIIMS 2015
Exam
AIIMS
Year
2015
Subject
Physics
Chapter
Rotational Motion

AIIMS 2015 · Physics · Rotational Motion

An air compressor is powered by a 200 rad / s electric motor using...

An air compressor is powered by a 200rad/s200 \mathrm{rad} / \mathrm{s} electric motor using a V-belt drive. The motor pulley is 8 cm8 \mathrm{~cm} in radius, and the tension in the V\mathrm{V}-belt is 135 N135 \mathrm{~N} on one side and 45 N45 \mathrm{~N} on the other. The power of the motor will be

Options

  1. A1.44 kW1.44 \mathrm{~kW}
  2. B14.4 kW14.4 \mathrm{~kW}
  3. C2.88 kW2.88 \mathrm{~kW}
  4. D28.8 kW28.8 \mathrm{~kW}

Correct answer

A. 1.44 kW1.44 \mathrm{~kW}

Step-by-step solution

Since the net force on the belt is the difference between the two tensions, the torque exerted by the motor on the belt is, τ=Fr=(135N−45N)(0.08m)=7.2Nm\begin{aligned} \tau& =F r=(135 \mathrm{ N}-45 \mathrm{ N})(0.08 \mathrm{ m})\\ & =7.2 \mathrm{ N} \mathrm{ m} \end{aligned} The poweroutputofthemotoristhereforepower output of the motor is thereforeP=τω=(72N⋅m)(200rad\mathrms−1)=1440W=1.44kW\begin{aligned}P & =\tau \omega=(72 \mathrm{ N} \cdot \mathrm{m}) \left(200 \mathrm{rad} \mathrms^{-1}\right)\\ & =1440 \mathrm{ W}=1.44 \mathrm{ kW} \end{aligned}$$
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