Dimensions of physical quantity are the powers which are raised to fundamental quantities in order to represent that physical quantity.

Dimensions of a Physical Quantity

Definition: The dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity.

Dimensions are essential in physics as they help in understanding the relationships between different physical quantities and are used in formulating equations and laws.

Explanation:

The dimensions of a physical quantity can be determined by analyzing the units in which the quantity is measured. Each base quantity has a specific unit, and the dimensions of a derived quantity are expressed in terms of these base units.

For example, let's consider the physical quantity of area. Area is a derived quantity that is calculated by multiplying length and width. The base quantities for length and width are L and L, respectively. Therefore, the dimensions of area would be expressed as L², where the exponent 2 represents the power to which the base quantity is raised.

Options:

a) The sum of the exponents of base quantities: This option is incorrect. The dimensions of a physical quantity are not determined by summing the exponents of base quantities. Rather, each base quantity has its own exponent that represents its dimension in the derived quantity.

b) The mean of the exponents of base quantities: This option is incorrect. The dimensions of a physical quantity are not determined by taking the mean of the exponents of base quantities. Each base quantity has a specific exponent that represents its dimension in the derived quantity.

c) The powers (or exponents) to which the base quantities are raised to represent that quantity: This option is correct. The dimensions of a physical quantity are determined by the powers (or exponents) to which the base quantities are raised to represent that quantity. Each base quantity has its own exponent that represents its dimension in the derived quantity.

d) The sum of all the number of base quantities: This option is incorrect. The dimensions of a physical quantity are not determined by summing the number of base quantities. The dimensions are determined by the specific exponents assigned to each base quantity.

In conclusion, the correct answer is option 'C' - the dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity.