A body of mass 5kg rests on a rough horizontal surface of coefficient of friction 0.2. The body is pulled through a distance of 10m by a horizontal force of 25N. The kinetic energy acquired by the body is (g= `10ms^(-2))`

Options

A. 250 J
B. 200 J
C. 150 J
D. 100 J

Answer

To solve the problem step by step, we will follow the principles of physics related to forces, friction, and work-energy theorem.

### Step 1: Calculate the Normal Force
The normal force (N) acting on the body can be calculated using the formula:
\[ N = mg \]
Where:
- \( m = 5 \, \text{kg} \) (mass of the body)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating:
\[ N = 5 \, \text{kg} \times 10 \, \text{m/s}^2 = 50 \, \text{N} \]

### Step 2: Calculate the Frictional Force
The frictional force (f) can be calculated using the formula:
\[ f = \mu N \]
Where:
- \( \mu = 0.2 \) (coefficient of friction)

Calculating:
\[ f = 0.2 \times 50 \, \text{N} = 10 \, \text{N} \]

### Step 3: Calculate the Net Force
The net force (F_net) acting on the body can be calculated by subtracting the frictional force from the applied force (F):
\[ F_{\text{net}} = F - f \]
Where:
- \( F = 25 \, \text{N} \) (applied force)

Calculating:
\[ F_{\text{net}} = 25 \, \text{N} - 10 \, \text{N} = 15 \, \text{N} \]

### Step 4: Calculate the Work Done on the Body
The work done (W) on the body can be calculated using the formula:
\[ W = F_{\text{net}} \times s \]
Where:
- \( s = 10 \, \text{m} \) (distance pulled)

Calculating:
\[ W = 15 \, \text{N} \times 10 \, \text{m} = 150 \, \text{J} \]

### Step 5: Calculate the Kinetic Energy Acquired by the Body
According to the work-energy theorem, the kinetic energy (KE) acquired by the body is equal to the work done on it:
\[ KE = W \]
Thus:
\[ KE = 150 \, \text{J} \]

### Final Answer
The kinetic energy acquired by the body is \( 150 \, \text{J} \).

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