Doubtclip is an AI tutor that turns any homework or exam doubt into a step-by-step whiteboard video lesson with diagrams, formulas, and voice explanation.

Which subjects and exams does it support?

It supports Physics, Chemistry, Mathematics/Calculus and related STEM doubts for school boards, JEE, NEET, and global high-school / undergrad practice.

How do I get a video solution?

Upload a photo of the question or paste the text, sign in, and Doubtclip generates a whiteboard-style explanation video you can watch and share.

Is Doubtclip available worldwide?

Yes. Doubtclip is a web app for students globally. Lessons are available in English and Hinglish.

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^3S^(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.

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

Both (A) and (R) are true but (R) is not the correct explanation of (A)

Units & Dimensions

JEE Main level, single correct, medium

83 of 149

Question 83 of 149

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 $\left(S\right)$ , if density of the liquid is $\rho$ and radius of the drop is $r$ , then $T=K\sqrt{\dfrac{\rho {r}^{3}}{{S}^{\dfrac{3}{2}}}}$ 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.

Show answer and solution

Answer: (D) (A) is false but (R) is true

Using dimensional analysis for the given equation,

T=K\sqrt{\dfrac{\rho {r}^{3}}{{S}^{\dfrac{3}{2}}}}

\Rightarrow \left[K\right]=\dfrac{\left[T\right]\left[{S}^{\dfrac{3}{4}}\right]}{\left[{\rho }^{\dfrac{1}{2}}\right]\left[{r}^{\dfrac{3}{2}}\right]} \Rightarrow \left[K\right]=\dfrac{\left[T\right]\left[{M}^{\dfrac{3}{4}}{T}^{-\dfrac{3}{2}}\right]}{\left[{M}^{\dfrac{1}{2}}{L}^{-\dfrac{3}{2}}\right]\left[{L}^{\dfrac{3}{2}}\right]} \Rightarrow \left[K\right]=\left[{M}^{\dfrac{1}{4}}{T}^{-\dfrac{1}{2}}\right]

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

\neq

Dimensions of R.H.S

∴

Option (D) is correct.

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Units & Dimensions (Dimensions), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.