A body is under the action of two mutually perpendicular forces of 3 N and 4 N. The resultant force acting on the body is

Options

A. 7N
B. 1N
C. 5N
D. zero

Answer

To find the resultant force acting on a body under the action of two mutually perpendicular forces of 3 N and 4 N, we can use the Pythagorean theorem. Here’s the step-by-step solution:

### Step 1: Identify the Forces
We have two forces:
- Force A = 3 N
- Force B = 4 N

### Step 2: Understand the Geometry
Since the forces are mutually perpendicular, we can visualize them as two sides of a right triangle, where:
- One side (A) is 3 N
- The other side (B) is 4 N

### Step 3: Apply the Pythagorean Theorem
The resultant force (R) can be calculated using the Pythagorean theorem:
\[ R = \sqrt{A^2 + B^2} \]

### Step 4: Substitute the Values
Substituting the values of A and B into the equation:
\[ R = \sqrt{(3 \, \text{N})^2 + (4 \, \text{N})^2} \]
\[ R = \sqrt{9 \, \text{N}^2 + 16 \, \text{N}^2} \]

### Step 5: Calculate the Result
Now, calculate the sum inside the square root:
\[ R = \sqrt{25 \, \text{N}^2} \]
\[ R = 5 \, \text{N} \]

### Conclusion
The resultant force acting on the body is **5 N**.

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