JEE Main202229 Jul 2022Morning ShiftPhysicsUnits and DimensionsActual
Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R) Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension S , if density of the liquid is ρ and radius of the drop is r , then T = K ρ r 3 S 3 2 is dimensionally correct, where K is dimensionless. Reason (R) : Using dimensional analysis we get R.H.S. having different dimension th
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
D. (A) is false but (R) is true
Step-by-step solution
Using dimensional analysis for the given equation, T = K ρ r 3 S 3 2 ⇒ K = T S 3 4 ρ 1 2 r 3 2 ⇒ K = T M 3 4 T - 3 2 M 1 2 L - 3 2 L 3 2 ⇒ K = M 1 4 T - 1 2 Therefore, K is not dimensionless. Hence, Assertion is false. For dimensional validity of the given equation, K can not be dimensionless. If it is dimensionless then Dimensions of L.H.S ≠ Dimensions of R.H.S ∴ Option (D) is correct.