Which of the following physical quantities has same SI unit as that of work?

Energy

The correct answer is option 4. Energy.

Work and energy are closely related concepts in physics. Here's an explanation of both terms and how they are interconnected:

1. Work:

In physics, work is defined as the product of the force applied to an object and the distance over which the force is applied. Mathematically, work (W) is given by the formula:

\[ W = \text{Force} \times \text{Distance} \times \cos(\theta) \]

where:

\( W \) is the work done,

\( \text{Force} \) is the force applied,

\( \text{Distance} \) is the distance over which the force is applied, and

\( \theta \) is the angle between the force vector and the displacement vector.

Work is a scalar quantity and is measured in joules (J) in the International System of Units (SI).

2. Energy:

Energy is the ability to do work. It exists in various forms such as kinetic energy, potential energy, thermal energy, etc.

Kinetic energy (\( KE \)) is the energy an object possesses due to its motion and is given by the formula:

\[ KE = \frac{1}{2} m v^2 \]

where:

\( m \) is the mass of the object, and

\( v \) is its velocity.

Potential energy (\( PE \)) is the energy an object possesses due to its position or configuration and is given by various formulas depending on the situation.

Energy is also a scalar quantity and is measured in joules (J) in the SI system.

The relationship between work and energy lies in the fact that when work is done on an object, it transfers energy to that object. Conversely, when work is done by an object, it loses energy. This principle is encapsulated in the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

In summary, work is the transfer of energy that occurs when a force is applied to move an object through a distance, and energy is the capacity to do work. They share the same unit (joule) and are fundamental concepts in physics, describing how objects interact and change in response to forces.