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JEE Mains · Physics · STD 11 - 1. units,dimensions and 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 \(T = k \sqrt{ pr ^{3} / s ^{3 / 2}}\) 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.

  1. A Both \((A)\) and \((R)\) are true and \((R)\) is the correct explanation of \((A)\)
  2. B Both \((A)\) and \((R)\) are true but \((R)\) is not the correct explanation of \((A)\)
  3. C \((A)\) is true but \((R)\) is false
  4. D \((A)\) is false but \((R)\) is true
Verified Solution

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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