Correct Answer - Option 1 : [M
1L
-1T
-2]
Concept:
-
Dimensional Formula: The dimensions of a physical quantity represent its nature.
- The dimension of Fundamental Quantities is known and the dimensional formula for other quantities is derived from fundamental units.
- Example:
- Finding Dimension of Density:
- The expression for density is Mass / Volume
- Mass is a fundamental unit with dimension M,
- Volume is a cube of length. So, Dimensional Formula for Length L3
- The dimension of density will be M / L3 = ML-3
For an equation to be dimensionally correct, the dimension of the equation in the left-hand side, and right-hand side should be equal.
Explanation:
Given, \(P = \frac{a+x}{b}\)
Left Hand Side is Pressure
Dimension of Pressure = [M1L-1T-2]
This should be the dimension of \( \frac{a+x}{b}\)
a + x is added, so dimension of both must be same
Dimension of \( \frac{a+x}{b}\) = Dimension of \( \frac{a}{b}\)
But Dimension of \( \frac{a+x}{b}\) = Dimesnion of pressure = [M1L-1T-2]
So, dimension of a/b is [M1L-1T-2]