GATE ME 2016 Set 1 — Question 40
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Engineering Mechanics → Statics → Free-Body Diagrams & Equilibrium
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Question
A block of mass rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is 0.25. The string can withstand a maximum force of 20 N. The maximum value of the mass () for which the string will not break and the block will be in static equilibrium is ____________ kg.Take and .Acceleration due to gravity
Correct answer
4.95 to 5.05
Solution
To find the maximum mass for which the block remains in static equilibrium, we consider the forces acting on the block along the inclined plane.The forces are:
1.Component of weight down the plane:
2.Tension in the string up the plane:
3.Frictional force:
The normal force is . The maximum static frictional force is .For the maximum mass , the block has a tendency to slide down the plane. Therefore, the frictional force acts up the plane to oppose this motion. At the limit of equilibrium:To maximize , we set to its maximum allowable value () and to its maximum static value ():Substituting the given values , , , and :Thus, the maximum mass for which the block remains in equilibrium is 5 kg.Continue learning with Success Tracker
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