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1.Units, Dimensions and Measurement
medium
Which of the following dimensions will be the same as that of time?
A$\frac CL$
B$\frac LR$
C$LC$
D$\frac RL$
(AIPMT-1996)
Solution
$R C = M L ^{2} T ^{-3} I ^{-2} \cdot M ^{-1} L ^{-2} T ^{4} I ^{2}= T$
$\sqrt{ L C }=\sqrt{ M L ^{2} T ^{-2} I ^{-2} \cdot M ^{-1} L ^{-2} T ^{4} I ^{2}}=\sqrt{ T ^{2}}= T$
$\frac{ L }{ R }=\frac{ M L ^{2} T ^{-2} I ^{-2}}{ M L ^{2} T ^{-3} I ^{-2}}= T$
$\sqrt{ L C }=\sqrt{ M L ^{2} T ^{-2} I ^{-2} \cdot M ^{-1} L ^{-2} T ^{4} I ^{2}}=\sqrt{ T ^{2}}= T$
$\frac{ L }{ R }=\frac{ M L ^{2} T ^{-2} I ^{-2}}{ M L ^{2} T ^{-3} I ^{-2}}= T$
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 | $IV$ $(ML ^2 T ^{-1})$ |
