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 $\mathrm{T}=\mathrm{k} \sqrt{\mathrm{pr}^{3} / \mathrm{s}^{3 / 2}}$ 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.

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

(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

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Units & Measurement

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 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.

(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✓ Correct

Answer: (D)

Solution

Check the dimensional consistency of the given formula. The dimension of surface tension

S

[M T^{- 2}]

. For the RHS:

\frac{ρ r ^{3}}{s ^{3/2}} = \frac{[ M L ^{- 3} ] ^{1/2} [ L ^{3/2} ]}{[ M T ^{- 2} ] ^{3/4}} = M^{1/2 - 3/4} L^{- 3/2 + 3/2} T^{3/2} = M^{- 1/4} T^{3/2}

. This does not match the dimension of time period

[T]

. Therefore, Assertion (A) is false (the formula is NOT dimensionally correct), while Reason (R) is true (RHS has different dimension than time period).

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Single correct option

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JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Units & Measurement

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