JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2023
- Medium
- MCQ
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\({\left[ T ^{-1}\right]=\left[ L ^1\right]^{ a }\left[ M ^{ 1 } L ^{-3}\right]^{ b }\left[\frac{ MLT ^{-2}}{ L }\right]^{ c }}\)
\(\Rightarrow T ^{-1}= M ^{ b + c } \cdot L ^{ a -3 b } \cdot T ^{-2 c}\)
\(c =\frac{1}{2}, b =-\frac{1}{2}, \quad a -3 b =0\)
\(a +\frac{3}{2}=0 \Rightarrow a =-\frac{3}{2}\)
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