Correct Option
The correct option is Pair 1
Explanation
Work done ($W$) by a constant force is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. Mathematically, $W = F \cdot d \cdot \cos \theta$, where $\theta$ is the angle between the force vector ($F$) and the displacement vector ($d$).
- Positive Work: When the force acts in the direction of motion ($0^\circ \leq \theta < 90^\circ$).
- Negative Work: When the force acts opposite to the direction of motion ($90^\circ < \theta \leq 180^\circ$).
- Zero Work: When the force is perpendicular to the displacement ($\theta = 90^\circ$).
Statement-wise Analysis
- Pair 1: Correct. When a body falls freely, the gravitational force acts downwards, and the displacement of the body is also downwards. Since the force and displacement are in the same direction ($\theta = 0^\circ$), the work done by gravity is positive.
- Pair 2: Incorrect. Kinetic friction always acts in the direction opposite to the relative motion of the object. Therefore, the angle between the frictional force and displacement is $180^\circ$. Consequently, the work done by friction is negative.
- Pair 3: Incorrect. When lifting a bucket, the applied force acts upwards to overcome gravity, and the displacement of the bucket is also upwards. Since the applied force and displacement are in the same direction ($\theta = 0^\circ$), the work done by the applied force is positive. (The work done by gravity in this case would be negative).
- Pair 4: Incorrect. For a satellite (like the Moon) orbiting the Earth in a circular path, the gravitational force acts towards the center of the Earth (centripetal force), while the instantaneous displacement is tangential to the orbit. The angle between the force and displacement is $90^\circ$. Therefore, the work done by Earth's gravity is zero.
Key Takeaway: The nature of work depends entirely on the angle ($\theta$) between the force and displacement vectors: it is positive if $\theta$ is acute, negative if $\theta$ is obtuse (opposing motion), and zero if the force is perpendicular to the displacement.