JEE Main 2022 · 29 Jul · Shift 1 · Physics Q31

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PhysicsSingle correct+4 / -1Question 31 of 90

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

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)

(A) is true but (R) is false

(A) is false but (R) is true

Answer and worked solution

Official answer: D

Dimensions. $\dfrac{\rho r^3}{S^{3/2}}$ has $[ML^{-3}][L^3]/[MT^{-2}]^{3/2}=M^{-1/2}T^3$ , so its square root is not a time. The formula is wrong (the correct one has S, not $S^{3/2}$ ), and the reason states exactly that.

(D)

Topics:Dimensional analysis Surface tension

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JEE Main 2022 · 29 Jul · Shift 1, Physics question 31