JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The frequency \((v)\) of an oscillating liquid drop may depend upon radius \((r)\) of the drop, density \((\rho)\) of liquid and the surface tension \((s)\) of the liquid as : \(v=r^{ a } \rho^{ b } s ^{ c }\). The values of \(a , b\) and \(c\) respectively are
- A \(\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)\)
- B \(\left(\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)\)
- C \(\left(\frac{3}{2}, \frac{1}{2},-\frac{1}{2}\right)\)
- D \(\left(-\frac{3}{2}, \frac{1}{2}, \frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\({\left[ T ^{-1}\right]=\left[ L ^1\right]^{ a }\left[ M ^{ 1 } L ^{-3}\right]^{ b }\left[\frac{ MLT ^{-2}}{ L }\right]^{ c }}\) \(\Rightarrow T ^{-1}= M ^{ b + c } \cdot L ^{ a -3 b } \cdot T ^{-2 c}\) \(c =\frac{1}{2}, b =-\frac{1}{2}, \quad a -3 b =0\)…
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