Correct Option
The correct option is (b).
Explanation
Work is defined as the scalar product of the force vector and the displacement vector. Mathematically, it is expressed as:
W = F d cos θ
Where F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the direction of the force and the direction of the displacement.
Statement-wise Analysis
- Statement 1 is Incorrect: When the force acts in the direction of displacement, the angle θ is 0°. Since cos 0° = 1, the work done is positive (W = +Fd). This represents the condition for maximum positive work.
- Statement 2 is Correct: When the force acts opposite to the direction of displacement, the angle θ is 180°. Since cos 180° = -1, the work done is negative (W = -Fd). This typically occurs with retarding forces such as friction or air resistance.
- Statement 3 is Incorrect: When the force acts perpendicular to the displacement, the angle θ is 90°. Since cos 90° = 0, the work done is zero. For example, the work done by gravity on an object moving horizontally is zero.
Key Takeaway: The nature of work depends entirely on the angle between force and displacement: it is positive for acute angles (0° ≤ θ < 90°), negative for obtuse angles (90° < θ ≤ 180°), and zero when the force is perpendicular to displacement (θ = 90°).