GATE 2021 ME (ME2) – Question 61

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

A block of negligible mass rests on a surface that is inclined at 30° to the horizontal plane as shown in the figure. When a vertical force of 900 N and a horizontal force of 750 N are applied, the block is just about to slide. The coefficient of static friction between the block and surface is _____ (round off to two decimal places).

Block on a 30-degree incline with a 900 N downward force and a 750 N horizontal leftward force. See the attached source image.

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Correct answer: 0.16 to 0.18

Explanation

The leftward force’s upslope component is 750 cos 30°, opposed by 900 sin 30° downslope. Net tendency is 199.519 N upslope, so friction acts downslope.

Normal force is 900 cos 30°+750 sin 30°=1154.423 N. Thus $\mu=199.519/1154.423=0.172830$, rounded to **0.17**.