The S.I. unit of work is ______ and energy is ______.

Explanation:

The S.I. Unit of Work and Energy

Definition: The S.I. unit (International System of Units) is the globally accepted standard for measuring various physical quantities. For work and energy, the unit is the same because they are closely related concepts in physics. The S.I. unit for both work and energy is the Joule (J).

Work: Work is defined as the transfer of energy that occurs when a force is applied to an object and the object moves in the direction of the force. Mathematically, work is expressed as:

Work (W) = Force (F) × Displacement (d) × cos(θ)

Where:

• F is the force applied (in Newtons).
• d is the displacement of the object (in meters).
• θ is the angle between the force and displacement.

The unit of force is Newton (N), and the unit of displacement is meter (m). Therefore, the unit of work becomes:

1 Joule (J) = 1 Newton (N) × 1 meter (m)

This means that 1 Joule of work is done when a force of 1 Newton moves an object through a distance of 1 meter in the direction of the force.

Energy: Energy is the capacity to perform work. It can exist in various forms, such as kinetic energy, potential energy, thermal energy, and so on. Since energy is the ability to do work, its unit is the same as that of work, which is the Joule (J).

For example:

• Kinetic Energy (KE): KE = (1/2) × mass (m) × velocity (v²)
• Potential Energy (PE): PE = mass (m) × gravitational acceleration (g) × height (h)

In all cases, the unit of energy remains the Joule (J).

Correct Option Analysis:

The correct option is:

Option 3: Joule; Joule

This is the correct answer because both work and energy share the same unit, which is the Joule (J) in the International System of Units. The Joule is derived from the basic units of force (Newton) and displacement (meter), as explained above.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Watt; Joule

This option is incorrect because the Watt (W) is not the unit of work. Instead, it is the unit of power, which is the rate at which work is done or energy is transferred. Mathematically, power is expressed as:

Power (P) = Work Done (W) / Time (t)

The unit of power is the Watt (W), where:

• 1 Watt = 1 Joule / 1 second

Thus, while the Joule is the correct unit for energy, the Watt is not the correct unit for work.

Option 2: Newton; Newton

This option is incorrect because the Newton (N) is the unit of force, not work or energy. As explained earlier, work involves the application of force over a displacement. The unit of force (Newton) contributes to the unit of work (Joule), but it is not the unit of work itself. Similarly, energy is not measured in Newtons.

Option 4: Joule; Newton

This option is incorrect because, while the Joule is the correct unit for work, the Newton is not the correct unit for energy. Energy, like work, is measured in Joules, as explained above.

Conclusion:

The S.I. unit of both work and energy is the Joule (J). This unit is derived from the basic physical quantities of force and displacement for work and from the ability to perform work for energy. The analysis of the other options highlights common misconceptions about the units of related physical quantities, such as power (Watt) and force (Newton). Understanding these distinctions is essential for clarity in physics and engineering applications.