GATE CE 2026 Set 1 — Question 50
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Structural Engineering → Statics & Rigid Bodies → Friction & Applications
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Question
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 , the value of the coefficient of static friction is ______ (rounded off to two decimal places).
Correct answer
0.39 to 0.44
Solution
Let be the weight of each block and be the coefficient of static friction.
At impending slip, block A moves down and block B moves to the right.
Forces on block A:
From equilibrium of block B:
Substituting from (1) into (2):
Dividing by :
Given , :
Solving for using the quadratic formula:
Since must be positive, .
Rounding to two decimal places, .
At impending slip, block A moves down and block B moves to the right.
Forces on block A:
- Normal force from the wall (horizontal)
- Friction force (upwards)
- Weight (downwards)
- Rod force (along the rod)
- Normal force from the floor (vertical)
- Friction force (leftwards)
- Weight (downwards)
- Rod force (along the rod)
From equilibrium of block B:
Substituting from (1) into (2):
Dividing by :
Given , :
Solving for using the quadratic formula:
Since must be positive, .
Rounding to two decimal places, .
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