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1.Units, Dimensions and Measurement
hard
If $C$ and $V$ represent capacity and voltage respectively then what are the dimensions of $\lambda,$ where $\frac{ C }{ V }=\lambda ?$
A$\left[ M ^{-2} L ^{-3} I ^{2} T ^{6}\right]$
B$\left[ M ^{-3} L ^{-4} I ^{3} T ^{7}\right]$
C$\left[ M ^{-1} L ^{-3} I ^{-2} T ^{-7}\right]$
D$\left[ M ^{-2} L ^{-4} I ^{3} T ^{7}\right]$
(JEE MAIN-2021)
Solution
$\lambda=\frac{ C }{ V }=\frac{ Q / V }{ V }=\frac{ Q }{ V ^{2}}$
$V =\frac{\text { work }}{ Q }$
$\lambda=\frac{ Q ^{3}}{(\text { work })^{2}}=\frac{( It )^{3}}{( F . s )^{2}}$
$=\frac{\left[ I ^{3} T ^{3}\right]}{\left[ ML ^{2} T ^{-2}\right]^{2}}=\left[ M ^{-2} L ^{-4} I ^{3} T ^{7}\right]$
$V =\frac{\text { work }}{ Q }$
$\lambda=\frac{ Q ^{3}}{(\text { work })^{2}}=\frac{( It )^{3}}{( F . s )^{2}}$
$=\frac{\left[ I ^{3} T ^{3}\right]}{\left[ ML ^{2} T ^{-2}\right]^{2}}=\left[ M ^{-2} L ^{-4} I ^{3} T ^{7}\right]$
Standard 11
Physics
Similar Questions
Match List $I$ with List $II$
| List $I$ | List $II$ |
| $A$ Spring constant | $I$ $(T ^{-1})$ |
| $B$ Angular speed | $II$ $(MT ^{-2})$ |
| $C$ Angular momentum | $III$ $(ML ^2)$ |
| $D$ Moment of Inertia | $IV$ $(ML ^2 T ^{-1})$ |
