GATE 2016 ME (ME1) – Question 40

Engineering Mechanics · Friction and its applications: belts, brakes, clutches, screw jack, wedge · 2 marks · Numerical answer

A block of mass m rests on an inclined plane and is tied by a string to the wall as shown. The coefficient of static friction is 0.25. The string can withstand 20 N. Find the maximum m for static equilibrium without breaking the string, in kg. Take cos θ = 0.8, sin θ = 0.6 and g = 10 m/s².

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Correct answer: 4.95 to 5.05

Explanation

At impending downward motion, friction acts up the slope with maximum μmgcosθ. The tension required is mg(sinθ−μcosθ)=10m(0.6−0.25·0.8)=4mN. Set this to the20N string limit to obtain **m=5kg**. A larger mass requires tension beyond the allowed maximum.