GATE ME 2022 Set 2 — Question 30
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Engineering Mechanics → Statics → Belt, Brake, Clutch & Screw Friction
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Question
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of each can be placed on the platforms. The number of discs placed on the left side platform is and that on the right side platform is .It is found that for and , a force (refer to part (i) of the figure) is just sufficient to initiate upward motion of the left side platform. If the force is removed then the minimum value of (refer to part (ii) of the figure) required to prevent downward motion of the left side platform is______ (in integer).
Correct answer
3 to 3
Solution
Case (i): discs on left, on right. Force on the right side of the rope initiates upward motion of the left platform.
Tension on left .
Tension on right .
Since left moves up, is the larger tension. Using belt friction formula: .Case (ii): Force is removed. discs on right. We want to prevent downward motion of the left platform.
Left side wants to move down, so is the larger tension.
, .
To prevent motion: .
The minimum integer value of is 3.
Tension on left .
Tension on right .
Since left moves up, is the larger tension. Using belt friction formula: .Case (ii): Force is removed. discs on right. We want to prevent downward motion of the left platform.
Left side wants to move down, so is the larger tension.
, .
To prevent motion: .
The minimum integer value of is 3.
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