Question

Identify the pair of physical quantities which have different dimensions.

• A. Wave number and Rydberg’s constant
• B. Stress and Coefficient of elasticity
• C. Coercivity and Magnetisation
• D. Specific heat capacity and Latent heat

Answer 1

The Correct Option is D

To identify the pair of physical quantities with different dimensions, we need to understand the dimensional analysis of each option provided.

1. Wave number and Rydberg’s constant:

   Wave number is defined as the reciprocal of the wavelength of a wave, typically expressed as the number of wave cycles per unit distance. The dimension of wave number is [M^0L^{-1}T^0].

   Rydberg's constant is used in atomic physics to describe the wavelengths of a spectral line in many chemical elements. It is also expressed in terms of wave number, hence has the same dimension [M^0L^{-1}T^0]. Both have the same dimensions.

2. Stress and Coefficient of elasticity:

   Stress is force per unit area with dimensions [ML^{-1}T^{-2}].

   Coefficient of elasticity, often referred to as the modulus of elasticity, is stress/strain. Since strain is dimensionless (ratio), the coefficient of elasticity has the same dimension as stress: [ML^{-1}T^{-2}]. Both have the same dimensions.

3. Coercivity and Magnetisation:

   Coercivity is the intensity of the magnetic field required to demagnetize a fully magnetized material, often measured in ampere per meter, with dimensions [IL^{-1}].

   Magnetisation is magnetic moment per unit volume, with the same dimension as magnetic field, also [IL^{-1}]. Both have the same dimensions.

4. Specific heat capacity and Latent heat:

   Specific heat capacity is the amount of heat required to change a unit mass of a substance by one degree in temperature, with dimensions [L^2T^{-2}K^{-1}].

   Latent heat is the heat required to convert a unit mass of a solid into liquid without change of temperature, with dimensions [L^2T^{-2}]. These dimensions are different because latent heat does not depend on temperature change, unlike specific heat capacity.

Therefore, the correct answer is the pair that refers to "Specific heat capacity and Latent heat" because they have different dimensions. The dimensions of specific heat capacity are [L^2T^{-2}K^{-1}] and latent heat are [L^2T^{-2}].