Question

A block of mass $4\,\text{kg}$ is placed on a horizontal surface having coefficients of static and kinetic friction as $0.5$ and $0.4$ respectively. If a force parallel to the horizontal surface of $4\,\text{N}$ is applied to the body, then the force of friction acting on the body will be
$\left[g = 10\,\text{m/s}^2\right]$

• A. $16\,\text{N}$
• B. $20\,\text{N}$
• C. $8\,\text{N}$
• D. $4\,\text{N}$

Hint:

Static friction adjusts itself up to its maximum value to prevent motion.

Answer 1

The Correct Option is D

Step 1: Calculate normal reaction.
\[ N = mg = 4 \times 10 = 40\,\text{N} \]

Step 2: Calculate maximum static friction.
\[ f_{\text{max}} = \mu_s N = 0.5 \times 40 = 20\,\text{N} \]

Step 3: Compare applied force with limiting friction.
Applied force $= 4\,\text{N}<f_{\text{max}} = 20\,\text{N}$
So the block does not move.

Step 4: Frictional force.
For static condition, friction equals the applied force.
\[ f = 4\,\text{N} \]

Step 5: Conclusion.
The force of friction acting on the block is $4\,\text{N}$.