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A body of mass m is kept on a rough horizontal surface (coefficient of friction = μ). Horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given F, where F is [NEET (Odisha) 2019]

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a

F = mg + μ mg

b

F = μ mg

c

F ≤ mg 1 + μ2

d

F = mg

answer is C.

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Detailed Solution

The situation can be drawn asThe frictional force, f = μN = μ mg (∵ N=mg)From free body diagram, the resultant force is|F|=N2+f2 ≤ (mg)2 + (μmg)2 = mg1 + μ2This is the minimum force required to move the object. But as the body is not moving.∴ F ≤ mg 1 + μ2

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