A block of mass 10 kg is placed on a rough horizontal surface having coefficient of friction μ = 0.5. If a horizontal force of 100 N is acting on it, then acceleration of the block will be

The correct answer is 5 m/s².

We are given the following information:

Mass of block, m = 10 kg
Coefficient of friction, μ = 0.5
Applied horizontal force, F = 100 N
Acceleration due to gravity, g = 10 m/s²

Step 1: Find the Normal Force (N)

Since the surface is horizontal and there is no vertical acceleration, the normal force equals the weight of the block:

N=mg=10\times 10=100\text{N}

Step 2: Find the Frictional Force (f)

The kinetic (sliding) friction force opposes the motion and is given by:

f=\mu N=0.5\times 100=50\text{N}

Step 3: Find the Net Force Acting on the Block

The applied force acts forward (100 N) and friction acts backward (50 N). So the net force is:

F_{\text{net}}=F-f=100-50=50\text{N}

Step 4: Apply Newton's Second Law to Find Acceleration

Using Newton's second law, F_{\text{net}}=ma, we solve for acceleration:

a=\frac{F_{\text{net}}}{m}=\frac{50}{10}=5\text{m/s²}

Conclusion: The net forward force on the block is 50 N, which gives it an acceleration of 5 m/s² in the direction of the applied force.