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Grade 11Mechanics

A 274-N plank, of length L = 6.23 m, rests on the ground and on a frictionless roller at the top of a wall of height h = 2.87 m (see Fig). The center of gravity of the plank is at its center. The plank remains in equilibrium for any value of θ
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

Profile image of Simran Bhatia
11 Years agoGrade 11
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1 Answer

Profile image of Aditi Chauhan
11 Years ago
The plank is in rotational equilibrium; therefore the net torque about the point say O must be equal to zero, that is,
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The plank is in horizontal equilibrium, therefore the frictional force must be equal to the horizontal component of normal force N , that is
236-471_1.PNG
236-1572_1.PNG
236-970_1.PNG