In the CGS system, the unit erg second (erg multiplied by second) is the unit of which physical quantity?

Introduction / Context:
Units in physics often reveal the nature of the physical quantity they measure. In the CGS system, energy is measured in ergs and time in seconds. When these units are combined as erg second, they represent a quantity with dimensions of energy multiplied by time. This question asks which physical quantity uses erg second as its unit.

Given Data / Assumptions:

• Energy in CGS is measured in ergs.
• Time is measured in seconds.
• The combined unit erg second has dimensions of energy multiplied by time.
• We compare this with known physical quantities such as momentum and Planck constant.

Concept / Approach:
Angular momentum and linear momentum involve mass, length and velocity, and their units are of the form mass times length squared per time or mass times length per time. Energy has units of mass times length squared per time squared. When we multiply energy by time, we obtain mass times length squared per time. This is the dimension of action, a quantity that appears in quantum mechanics, and of Planck constant h. In the CGS system, Planck constant is often expressed in erg second. Therefore, the unit erg second corresponds to Planck constant or more generally to action.

Step-by-Step Solution:
Step 1: Write the CGS unit of energy as 1 erg, which has dimensions of mass times length squared per time squared. Step 2: Multiply energy by time to get erg second, which has dimensions mass times length squared per time. Step 3: Recall that Planck constant h connects energy and frequency through the relation E = h * f, so h has units of energy divided by frequency. Step 4: Frequency has units of 1 divided by time, so h as energy divided by frequency has units of energy times time. Step 5: Therefore, Planck constant in CGS units is measured in erg second, making erg second the unit of action or Planck constant.

Verification / Alternative check:
Look at standard values: in CGS, Planck constant h is often written as approximately 6.63 times 10 to the power minus 27 erg second. In SI, the same constant is expressed in joule second, showing that in both systems the unit is energy multiplied by time. Linear momentum uses gram centimetre per second, and angular momentum uses gram centimetre squared per second, which are clearly different from erg second. This confirms that erg second belongs to Planck constant and action, not to momentum or pure energy.

Why Other Options Are Wrong:
Angular momentum has units mass times length squared per time, which in CGS is gram centimetre squared per second, not erg second.
Linear momentum has units mass times length per time, that is gram centimetre per second.
Energy alone uses ergs, not erg second, and power uses energy per time, not energy times time.

Common Pitfalls:
Students sometimes see the word erg and immediately think of energy, ignoring the extra factor of second. Others group angular momentum and action together because they have similar dimensions in SI, but in CGS the presence of explicit ergs makes it clear that energy is involved. Always check the dimensions carefully and remember that Planck constant links energy and time or energy and frequency, so its unit is energy multiplied by time.

Final Answer:
The unit erg second in the CGS system is used for Planck constant or action.