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A body of mass m is kept on a rough horizontal surface (coefficient of friction = μ). A 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 by F, where F is

1. |F| = mg
2. |F| = μmg
3. |F| ≤ mg
4. |F| ≤ mg√(1 + μ²)

Correct answer: |F| ≤ mg√(1 + μ²)

Solution

The normal reaction and frictional force are perpendicular to each other. The resultant force is the vector sum of these two forces, which gives |F| = √(N² + f²). Here, N = mg and f ≤ μN. Substituting these, we get |F| ≤ mg√(1 + μ²).

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