GATE 2026 CE (CE1) – Question 50

Engineering Mechanics · Friction and its applications · 2 marks · Numerical answer

Two identical blocks A and B are connected by a rigid rod. The blocks rest against vertical and horizontal planes, as shown in the figure. The coefficient of static friction at the vertical and horizontal planes is the same. If the sliding impends when $\theta = 45°$, the value of the coefficient of static friction is ______ (*rounded off to two decimal places*).

Block A rests against a vertical wall at the top and block B rests on a horizontal floor at the bottom right. A rigid rod joins them and makes an angle $\theta$ with the horizontal.

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Correct answer: 0.40 to 0.42

Explanation

Let each block weigh $W$ and the rod force be $F$ along the rod. For block A, the wall gives $N_A = F\cos\theta$, and vertically $\mu N_A + F\sin\theta = W$. For block B, $N_B = W + F\sin\theta$ and $\mu N_B = F\cos\theta$. Eliminating $W$ and $F$ gives $\mu^2\cos\theta + 2\mu\sin\theta - \cos\theta = 0$. With $\theta = 45°$ this is $\mu^2 + 2\mu - 1 = 0$, so $\mu = \sqrt{2} - 1 = 0.41$.