NEETPhysicsUnits and Dimensions
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The product of magnetic permeability ( ₀ ) and electric permittivity ( ₀ ) has the dimensional formula [ L ⁻² T ^2] . Reason (R): The speed of electromagnetic waves in vacuum is given by c = 1 ₀ ₀ . In the light of the above statements, choose the most appropriate answer from the options given belo
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
Step-by-step solution
The speed of electromagnetic waves in vacuum is given by the relation c = 1 ₀ ₀ . Squaring both sides, we get c^2 = 1 ₀ ₀ , which implies ₀ ₀ = 1 c^2 . The dimensional formula for the speed of light c is [ LT ⁻¹] . Therefore, the dimensional formula for c^2 is [ L ^2 T ⁻²] . Thus, the dimensional formula for the product ₀ ₀ is 1 [ L ^2 T ⁻²] = [ L ⁻² T ^2] . Hence, Assertion (A) is true. Reason (R) is also true and provides the exact formula needed to derive the dimensions in the Assertion, making it the correct ex