Q. IF $L,\ C$ and $R$ denote the inductance, capacitance and resistance respectively, the dimensional formula for $C^{2}LR$ is
A) $\lbrack ML^{- 2}T^{- 1}I^{0}\rbrack$
B) $\lbrack M^{0}L^{0}T^{3}I^{0}\rbrack$
C) $\lbrack M^{- 1}L^{- 2}T^{6\ }I^{2}\rbrack$
D) $\lbrack M^{0}L^{0}T^{2}I^{0}\rbrack$
Explanation
$C^{2}LR = \left\lbrack C^{2}L^{2} \right\rbrack \times \ \left\lbrack \frac{R}{L} \right\rbrack = \left\lbrack T^{4} \right\rbrack \times \ \left\lbrack \frac{1}{T} \right\rbrack = \lbrack T^{3}\rbrack$ As $\left\lbrack \frac{L}{R} \right\rbrack = T$ and $\sqrt{LC} = T$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.