Which one of the following does not have the same dimensions.

plank constant and energy

The correct answer is Option (4) → plank constant and energy

To determine which of the given pairs does not have the same dimensions, let's analyze each pair:

1. Work and Energy:

Both work and energy have the same dimensions. In the International System of Units (SI), both work and energy are measured in joules (J), which have dimensions of \([M L^2 T^{-2}]\).

2. Angle and Strain:

Angle is a dimensionless quantity and does not have any dimensions. Strain, on the other hand, is the ratio of change in dimension to the original dimension and is dimensionless as well. Therefore, both angle and strain are dimensionless quantities.

3. Relative Density and Refractive Index:

Relative density is the ratio of the density of a substance to the density of a reference substance (usually water). Since it is a ratio of two quantities with the same dimensions, it is dimensionless. Refractive index (\(n\)) is also dimensionless and represents the ratio of the speed of light in a vacuum to the speed of light in a medium. Therefore, both relative density and refractive index are dimensionless.

4. Planck Constant and Energy:

The Planck constant (\(h\)) has dimensions of \([M L^2 T^{-1}]\) in the International System of Units (SI). Energy has dimensions of \([M L^2 T^{-2}]\). Therefore, the dimensions of the Planck constant and energy are different.

Based on the analysis, the pair that does not have the same dimensions is: Planck constant and Energy