In the MKS system of units (metre–kilogram–second), which of the following is the standard unit of energy?

Introduction / Context:
Different unit systems have been used historically in physics, such as the CGS system and the MKS system. The modern SI system is built on the MKS base units. Knowing which unit belongs to which system is important when reading formulas, converting units, and solving numerical problems. This question asks for the standard unit of energy in the MKS system.

Given Data / Assumptions:

• The MKS system uses metre, kilogram, and second as base units.
• Energy is a derived quantity related to work, force, and distance.
• Options include joule, ohm, erg, and volt.
• Ohm and volt are known electrical units, and erg is associated with the CGS system.

Concept / Approach:
In the MKS and SI systems, the unit of energy is the joule. One joule is defined as the work done when a force of one newton moves a body through one metre in the direction of the force. In base units, this corresponds to kg * m^2 / s^2. The erg is a much smaller unit of energy used in the CGS system, where base units are centimetre, gram, and second. Ohm is the unit of electrical resistance, and volt is the unit of electric potential difference, not energy.

Step-by-Step Solution:
Step 1: Recall that in the MKS system, force is measured in newtons, with 1 N = 1 kg * m / s^2. Step 2: Work or energy is defined as force times distance, so W = F * s, giving units of kg * m^2 / s^2. Step 3: The name assigned to the unit kg * m^2 / s^2 in the MKS and SI systems is joule, symbol J. Step 4: Erg is the CGS unit of energy and equals 10^-7 joule, so it is not the MKS unit. Step 5: Ohm and volt are units of electrical resistance and potential difference respectively, and do not directly represent energy.

Verification / Alternative check:
All modern physics textbooks and scientific references express mechanical, electrical, and thermal energy in joules when using SI units. For example, electrical energy may be written as E = V * I * t in joules when V is in volts, I in amperes, and t in seconds. Historical literature using the CGS system expresses the same quantity in ergs, but that system has largely been replaced by MKS and SI units in education and industry.

Why Other Options Are Wrong:
Ohm: Measures electrical resistance, defined as volt per ampere, and not an energy unit. Erg: The CGS unit of energy, not the standard unit in the MKS system. Volt: Measures electric potential difference or electromotive force, not energy itself.

Common Pitfalls:
Some learners see ohm or volt in energy related formulas and mistakenly think they are energy units. It helps to remember that energy usually appears with the symbol J in SI, representing joules. Another confusion is between MKS and CGS systems, where the same physical quantity has different named units; understanding the base units behind each system clarifies these differences.

Final Answer:
In the MKS system of units, the standard unit of energy is the joule.