Resultant of two perpendicular forces in engineering mechanics: If two forces of 3 kg and 4 kg act at right angles to each other, what is the magnitude of their single resultant force (use the parallelogram/Pythagorean relation and keep the given “kg” unit as stated in the problem)?

Introduction / Context:
When two forces act at right angles (perpendicular) to each other, their resultant is obtained by vector addition using the Pythagorean relation. This basic statics concept appears throughout engineering mechanics, machine design, and structural analysis.

Given Data / Assumptions:

• Magnitude of first force = 3 kg (treated as kilogram-force as stated).
• Magnitude of second force = 4 kg.
• The angle between the forces = 90 degrees.
• Forces are coplanar and concurrent at a point.

Concept / Approach:

For two perpendicular vectors of magnitudes P and Q, the resultant R satisfies R^2 = P^2 + Q^2. This is the parallelogram (or triangle) law of forces specialized to a right angle, reducing to the Pythagorean theorem.

Step-by-Step Solution:

Verification / Alternative check:

The 3–4–5 right triangle is a classic integer triple; it frequently appears in mechanics problems. Using vector components in orthogonal axes yields the same result.

Why Other Options Are Wrong:

7 kg (a) incorrectly sums magnitudes without direction; 1 kg (b) and 1/7 kg (d) are arbitrary; “None of these” (e) is unnecessary because 5 kg exactly matches the computed resultant.

Common Pitfalls:

Adding magnitudes directly without recognizing direction; forgetting that the resultant of orthogonal vectors uses the square root of the sum of squares.

Final Answer:

5 kg