A uniform force of 4 N acts on a body of mass 10 kg for a distance of 2.0 m . The kinetic energy acquired by the body is

Options

A. 16 J
B. `32xx10^8` erg
C. 8 J
D. 32 erg

Answer

To solve the problem, we will use the concepts of Newton's second law of motion and the work-energy theorem. Here’s a step-by-step solution:

### Step 1: Identify the given data
- Force (F) = 4 N
- Mass (m) = 10 kg
- Distance (s) = 2 m

### Step 2: Calculate the acceleration
Using Newton's second law, we know that:
\[ F = m \cdot a \]
Where:
- \( a \) is the acceleration.

Rearranging the formula to find acceleration:
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{4 \, \text{N}}{10 \, \text{kg}} = 0.4 \, \text{m/s}^2 \]

### Step 3: Use the work-energy principle
The work done on the body is equal to the change in kinetic energy. The work done (W) can be calculated using the formula:
\[ W = F \cdot s \]

Substituting the values:
\[ W = 4 \, \text{N} \cdot 2 \, \text{m} = 8 \, \text{J} \]

### Step 4: Conclusion
The kinetic energy acquired by the body is equal to the work done on it:
\[ \text{Kinetic Energy} = W = 8 \, \text{J} \]

Thus, the kinetic energy acquired by the body is **8 Joules**.

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