Question

We know from our knowledge of units and dimensional analysis that base quantities are physical quantities that cannot be defined in terms of other units. So, base quantities are basically those physical quantities that cannot be derived from other physical quantities.

Answer 1

Hint: We know from our knowledge of units and dimensional analysis that base quantities are physical quantities that cannot be defined in terms of other units. So, base quantities are basically those physical quantities that cannot be derived from other physical quantities.

Complete step by step answer:
We can start the solution by the method of elimination of options.
We know that power of a body is defined as the rate of doing work of the body. Mathematically it is the product of the force of a body and the velocity of the body. Thus the power can be expressed as force multiplied by velocity that is $P = Nm{s^{ - 1}}$. Since, this can be expressed in terms of different units; hence it is not a base quantity.

The momentum of a body is defined as the quantity of motion contained in a body. Mathematically it is the product of mass of the body and velocity of the body. Thus, momentum can be expressed as the mass multiplied by the velocity that is $p = kgm{s^{ - 1}}$. Since, this can be expressed in terms of different units; hence it is not a base quantity.

Latent heat is defined as the heat required in converting a solid into a liquid or vapour, or a liquid into a vapour, without any change in temperature. Mathematically it is expressed as the ratio between the amount of heat and mass of the substance. Thus, latent heat can be expressed as the amount of heat of the body divided by the mass of the body that is $L = cal/kg$. Since, this can be expressed in terms of different units; hence it is not a base quantity.

Radian is defined as the angle made when the radius of a circle is wrapped around the same circle. Mathematically, one radian is defined as $rad = \dfrac{{180}}{\pi }$. Since, this cannot be expressed in terms of different units; hence it is a base quantity.
Thus, the correct answer to this question is (D).

Note: If any quantity is a base quantity it doesn’t mean that it does not have different units. Length is a base quantity which can be expressed in different units like inches or metres.