A body of mass 2 kg is kept by pressing to a vertical wall by a force of 100 N. The friction between wall and body is 0.3. Then the frictional force is equal to

The correct answer is 20 N.

This problem involves a body pressed against a vertical wall. Before jumping into calculations, it is essential to understand the concept of limiting friction vs. actual (static) friction.

Given Data:
Mass of body, m = 2 kg
Applied (pressing) force, F = 100 N (horizontal, into the wall)
Coefficient of friction, μ = 0.3
Acceleration due to gravity, g = 10 m/s²

Step 1: Identify the Normal Reaction

The body is pressed horizontally against the wall. The wall pushes back with a Normal Reaction (N) equal and opposite to the applied pressing force:

N = F = 100 N

Step 2: Calculate the Maximum (Limiting) Friction Available

The maximum static friction the wall can provide is:

f_{\max }=\mu \times N=0.3\times 100=\mathrm{30\; N}

Step 3: Identify the Force That Friction Must Balance

The body is in equilibrium (not sliding). The only downward force acting on the body is its weight:

W=m\times g=2\times 10=\mathrm{20\; N}

Step 4: Apply the Key Concept — Static Friction is Self-Adjusting

Static friction does not automatically equal μN. It is self-adjusting — it adjusts itself to exactly balance the applied force (up to its maximum limit).

Here, the body tends to slide downward due to gravity (weight = 20 N). The friction acts upward to prevent this sliding.

Since the weight (20 N) is less than the maximum available friction (30 N), the body remains in equilibrium, and friction only needs to balance the weight:

f_{\mathrm{actual}}=W=\mathrm{20\; N}

Step 5: Conclusion

The actual frictional force acting on the body is equal to its weight, i.e., 20 N (acting upward along the wall). The maximum friction available (30 N) is never fully utilized because the body is in static equilibrium with just 20 N of friction needed.

⚠️ Common Mistake to Avoid: Many students directly calculate friction as μN = 0.3 × 100 = 30 N. This is the limiting friction (maximum possible), not the actual friction. Since the body is in equilibrium, actual friction = weight of body = 20 N.