Which of the following is the SI unit of work done?

Question

Examoogle · Accepted Answer

The correct answer is Option D: Joule. The SI unit of work done and energy is the joule (symbol: J). One joule is defined as the amount of work done by a force of one newton displacing an object through a distance of one metre in the direction of the applied force.

Step-by-Step Solution & Concepts:
The SI unit of work done and energy is the joule (symbol: J). One joule is defined as the amount of work done by a force of one newton displacing an object through a distance of one metre in the direction of the applied force.

Working Principle: Work ($W$) is mathematically defined as the scalar (dot) product of the applied force vector ($\vec{F}$) and the displacement vector ($\vec{s}$). That is, $W = F \cdot s \cdot \cos(	heta)$, where $	heta$ is the angle between the force and displacement vectors. Because force is measured in newtons (N) and displacement in metres (m), the SI unit of work is newton-metre ($N\cdot m$), which is officially named the joule (J) in honor of the physicist James Prescott Joule.

Key Formulas: $W = F \cdot s \cdot \cos(	heta)$ — Work done by a constant force; $1 	ext{ J} = 1 	ext{ N} \cdot 	ext{m} = 1 	ext{ kg} \cdot 	ext{m}^2 \cdot 	ext{s}^{-2}$ — SI unit breakdown

Key Points: Work is a scalar quantity, although it is the dot product of two vector quantities (force and displacement).; The SI unit of work is the Joule (J), named after the English physicist James Prescott Joule.; 1 Joule of work is done when a force of 1 Newton displaces a body by 1 metre in the direction of the force.; Erg is the CGS unit of work ($1 	ext{ J} = 10^7 	ext{ ergs}$).

Advantages: Standardized global system (SI) ensures unambiguous scientific communication.

Applications: Calculating mechanical energy transferred to or from a system.; Engineering design involving torque, power, and structural loads.

Additional Info: Option A (Erg): CGS unit of work/energy.. Option B (Metre): SI unit of length/displacement.. Option C (Newton): SI unit of force.. Option D (Joule): SI unit of work and energy.

Answer: D is correct — Joule is the SI unit of work done.

Exam Tip: Always remember that work and energy share the exact same SI unit (Joule) and dimensional formula ($[ML^2T^{-2}]$).

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