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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 cot $(θ /2)$ is

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not dependent on

μ

less than

μ

greater than

μ

equal to

μ

answer is B.

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Detailed Solution

mg \sin θ > f

then the block moves along the horizontal surface

Question Image

Frictional force $= f = μ N$

but $N + mgcos θ = mg$

$N = mg (1 - \cos θ)$

$f = μ mg (1 - \cos θ)$

$\Rightarrow mg \sin θ > μ mg (1 - \cos θ)$

$2 \sin θ /2 cos θ /2 > (μ {sin}^{2} θ /2) \times 2$

$cot θ /2 > μ$

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