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GATE 2026 ME – Question 48

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

A block of 50 kg mass is on an inclined plane. The block is connected to another hanging mass M by an inextensible massless string through two massless pulleys as shown in the figure below. The coefficient of static friction between the block and the inclined plane is 0.3. Neglecting pulley friction, the minimum value of M required to start the upward motion of the block is ________ kg (*rounded off to 1 decimal place*).

A 50 kg block on a plane inclined at 30°. A string from the block passes over a small pulley and then a larger pulley at the top of the incline, and a mass M hangs from its end.

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Correct answer: 37.81 to 38.19

Explanation

To start the block moving up the plane, the string tension must overcome the component of the weight along the plane plus the friction: $T = mg(\sin 30° + \mu\cos 30°) = 50g(0.5 + 0.3 \times 0.866) = 50g \times 0.7598$. The hanging mass gives $T = Mg$, so $M = 50 \times 0.7598 = 38.0$ kg.