A mass m rests on a rough horizontal surface (coefficient of friction μ). A horizontal force is applied but the object remains stationary. The magnitude F of the resultant of its normal force and frictional force obeys:
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Question

A mass m rests on a rough horizontal surface (coefficient of friction μ). A horizontal force is applied but the object remains stationary. The magnitude F of the resultant of its normal force and frictional force obeys:

Options

G1 Physics · Accepted Answer

Vertical equilibrium gives N=mg. The static friction magnitude satisfies 0≤f≤μmg. The resultant contact force is √(N²+f²), so |F|≤√[(mg)²+(μmg)²]=mg√(1+μ²). Answer: C.