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 surface tension (S), if density of the liquid is $p$ and radius of the drop is $r$, then $T=k\sqrt{p{r}^3/s^{3/2}}$ is dimensionally correct, where $K$ is dimensionless.
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension 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

Answer: (D)

$T=k\sqrt{\frac{\rho r^3}{s^{3/2}}}$
Dimensions of RHS
$\frac{\left[M^{1/2}{L}^{-3/2}\right]\left[L^{3/2}\right]}{{\left[M{T}^{-2}\right]}^{3/4}}=M^{1/8}{L}^0{T}^{3/2}$
Dimensions of L.H.S $\ne$ Dimensions of R.H.S