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GATE 2016 ME (ME3) – Question 41

Engineering Mechanics · Impulse and momentum, energy formulations · 2 marks · Numerical answer

A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed v of the disc when it reaches position B is _________ m/s. Acceleration due to gravity g = 10 m/s2. 200 N 100 N

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Correct answer: 19.9 to 20.1

Explanation

For rolling without slip, ω=v/r and I=mr²/2. Conservation of energy gives mgH=mv²/2+Iω²/2=3mv²/4. With g=10m/s²,H=30m, v=√(4gH/3)=**20m/s**. Static friction does no net work in ideal rolling.