JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2022
- Medium
- MCQ
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.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \((A)\) is false but \((R)\) is true
Step-by-step Solution
Detailed explanation
\(T=k \sqrt{\frac{\rho r^{3}}{s^{3 / 2}}}\)
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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