Question

The resultant of two forces P & Q ( such that P > Q) acting along the same straight line but in opposite direction, is given by

• A. \(P + Q\)
• B. \(P - Q\)
• C. \(P \times Q\)
• D. \(\frac{P - Q}{2}\)

Hint:

For collinear forces:
- Same direction: Add magnitudes (\(P + Q\)).
- Opposite directions: Subtract smaller magnitude from larger (\(P - Q\)).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Forces are vector quantities. When forces act along a common collinear line of action, their resultant can be determined using simple algebraic addition by assigning directional signs.

Step 3: Detailed Explanation:
Let the straight line of action be along the x-axis.
Let force \(P\) act in the positive direction:
\[ \vec{P} = P\hat{i} \] Let force \(Q\) act in the opposite (negative) direction:
\[ \vec{Q} = -Q\hat{i} \] The resultant vector \(\vec{R}\) is the vector sum of these two forces:
\[ \vec{R} = \vec{P} + \vec{Q} \] \[ \vec{R} = (P - Q)\hat{i} \] Since \(P \gt Q\), the magnitude of the resultant force is:
\[ R = P - Q \] The resultant force acts in the direction of the larger force \(P\).

Step 4: Final Answer:
The correct option is 2, which corresponds to \(P - Q\).