Correct Option
The correct option is (c).
Explanation
In physics, work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. Since work represents a transfer of energy, both work and energy share the same physical dimensions and units within the International System of Units (SI).
Statement-wise Analysis:
- Statement 1 is Correct: The standard SI unit of work is the Joule (symbol: J). It is a derived unit named after the physicist James Prescott Joule.
- Statement 2 is Incorrect: By definition, 1 Joule is the amount of work done when a force of 1 Newton displaces an object by 1 metre in the direction of the force ($1 \text{ J} = 1 \text{ N} \times 1 \text{ m}$). The statement incorrectly specifies the distance as 1 centimetre.
- Statement 3 is Correct: Energy is scientifically defined as the capacity to do work. Therefore, work and energy are physically equivalent quantities in terms of measurement, and they share the same SI unit, the Joule.
Key Takeaway:
The SI unit of work is the Joule, which is equivalent to one Newton-metre ($1 \text{ N} \cdot \text{m}$). Work and Energy possess identical dimensional formulas ($[ML^2T^{-2}]$) and units.