Question

Two forces acting at a point of a body are equilibrium if and only if they
(A) are equal in magnitude
(B) have same direction
(C) have opposite direction
(D) act along the same straight line
(E) are not equal in magnitude but have same direction
Choose the correct answer from the options given below:

• A. (A), (C) and (D) only
• B. (A), (B), (D) and (E) only
• C. (B), (C) and (D) only
• D. (A), (C), (D) and (E) only

Hint:

Think of a tug-of-war. For the rope to stay still (in equilibrium), the two teams must pull with the same force (equal magnitude) in perfectly opposite directions along the line of the rope. All three conditions (equal magnitude, opposite direction, same line of action) are necessary.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For a point body (or a single point on a rigid body) to be in equilibrium under the action of forces, the net force (vector sum of all forces) must be zero. This is Newton's First Law. We need to find the conditions for two forces, \( \vec{F}_1 \) and \( \vec{F}_2 \), such that their vector sum is zero.
Step 2: Key Formula or Approach:
The condition for equilibrium is: \[ \vec{F}_{net} = \vec{F}_1 + \vec{F}_2 = \vec{0} \] This vector equation implies conditions on the magnitude and direction of the two forces.
Step 3: Detailed Explanation:
From the equilibrium condition \( \vec{F}_1 + \vec{F}_2 = \vec{0} \), we can write \( \vec{F}_1 = -\vec{F}_2 \). Let's analyze what this relationship means:
Magnitude: The magnitude of a vector is always non-negative. Taking the magnitude of both sides: \( |\vec{F}_1| = |-\vec{F}_2| = |\vec{F}_2| \). This means the forces must be equal in magnitude. So, statement (A) is true. Statement (E) is false.
Direction: The negative sign indicates that the vector \( \vec{F}_1 \) points in the exact opposite direction to the vector \( \vec{F}_2 \). So, they must have opposite directions. Statement (C) is true. Statement (B) is false.
Line of Action: For the vectors to be exactly opposite, they must lie along the same straight line. This is also known as being collinear. So, statement (D) is true.
Step 4: Final Answer:
For two forces to be in equilibrium, they must be equal in magnitude, opposite in direction, and act along the same straight line. Therefore, statements (A), (C), and (D) are all required.