A cubical block of mass 'm' rests on rough horizontal surface. $μ$ is coefficient of static friction between block and the surface. A force "mg" acting on cube at an angle " $θ$ " with vertical side of cube pulls the block. if the block is to be pulled along the surface then the value of $c o t (θ / 2)$ is

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greater than $μ$

less than $μ$

not dependent on $μ$

equal to $μ$

answer is B.

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Detailed Solution

For balancing the forces:

F sinθ=μ(mg − Fcosθ);

F=mg

⇒sinθ/(1−cosθ) = μ

⇒cot(θ/2) = μ

To move the body, cot(θ/2)>μ

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