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STD 11 - 1. units,dimensions and measurement — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 1. units,dimensions and measurement4 Marks
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 $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ 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.

✓

Answer

$T=k \sqrt{\frac{\rho r^{3}}{s^{3 / 2}}}$

Dimensions of $RHS =\frac{\left[ M ^{1 / 2} L ^{-3 / 2}\right]\left[ L ^{3 / 2}\right]}{\left[ MT ^{-2}\right]^{3 / 4}}= M ^{1 / 3} L ^{0} T ^{3 / 2}$

Dimensions of L.H.S $\neq$ Dimensions of R.H.S

$\therefore$ option (D)

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