Question

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 surf ace tension (S), if density of the liquid is ρ and radius of the drop is r, then \(T=K\sqrt {\frac {ρr^3}{S^{\frac 32}}}\) is dimensionally correct, where K is dimensionless.
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A)
• B. Both (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

Answer 1

The Correct Option is D

\([\frac {ρr^3}{T^{\frac 32}}]=\frac {[ML^{−3}][L^3]}{[ML^0T^{−2}]^{\frac 32}}≠[T]\)
As the equation for first statement is wrong dimensionally.
⇒A is false and R is true.

So, the correct option is (D): (A) is false but (R) is true.