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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{\frac{ρr^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.

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true

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

Solution

Assertion (A) correctly states the relationship between the time period of oscillation of a liquid drop and the factors of surface tension, density, and radius, which can be derived dimensionally. However, Reason (R) claims that the dimensions do not match, which is incorrect; thus, while both statements are true, R does not explain A.

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