Question

100 N horizontal force is applied on a body of mass 10 kg kept on a rough horizontal surface. If coefficient of friction between the surface and the body is 0.5, then the acceleration produced in the body will be

• A. 0
• B. 5 m/s\(^2\)
• C. 5.2 m/s\(^2\)
• D. 10 m/s\(^2\)

Hint:

Always subtract the frictional force from the applied force when calculating the net force in frictional systems.

Answer 1

The Correct Option is C

Step 1: Understanding the forces.
The applied force is 100 N, and the frictional force is
given by \( f_{\text{friction}} = \mu \times N \), where \( \mu \) is the coefficient of friction and \( N \) is the normal force.
For a horizontal surface, the normal force is equal to the weight of the object, \( N = mg = 10 \times 9.8 = 98 \, \text{N} \). The frictional force is: \[ f_{\text{friction}} = 0.5 \times 98 = 49 \, \text{N} \]
Step 2: Net force and acceleration.
The net force acting on the body is the applied force minus the frictional force: \[ F_{\text{net}} = 100 - 49 = 51 \, \text{N} \] Now, using Newton's second law: \[ F_{\text{net}} = ma \quad \Rightarrow \quad a = \frac{F_{\text{net}}}{m} = \frac{51}{10} = 5.2 \, \text{m/s}^2 \] Thus, the correct answer is
(C) 5.2 m/s\(^2\)
.