Question

If $R$ is resistance, $L$ is inductance, $C$ is capacitance, $H$ is latent heat, and $s$ is specific heat, then match the quantity given in Column I with the dimensions given in Column II.

Column I		Column II
i	$L C$	a	$L^{2} T^{-2}$
ii	$L R$	b	$L^{2} T^{-2} K^{-1}$
iii	$H$	c	$T^{2}$
iv	$s$	d	$M^{2} L^{4} T^{-5} A^{-4}$

• A. $i \rightarrow c ; i \rightarrow d ; iii \rightarrow a; iv \rightarrow b$
• B. $i \rightarrow d ; i \rightarrow c ; iii \rightarrow a; iv \rightarrow b$
• C. $i \rightarrow b ; i \rightarrow a ; iii \rightarrow c; iv \rightarrow b$
• D. $i \rightarrow b ; i \rightarrow c ; iii \rightarrow d; iv \rightarrow a$

Answer 1

Answer: (A)

(i) $[L C]=\left[\frac{L}{R} R C\right]=T^{2}$
(ii) $[L R] =\left[\frac{L}{R} R^{2}\right]=T\left[R^{2}\right]$
$=T\left[\frac{V}{I}\right]^{2}=T\left[\frac{W}{Q I}\right]^{2}$
$=T\left(\frac{W}{I^{2} t}\right)^{2}=T\left(\frac{M L^{2} T^{-2}}{A^{2} T}\right)^{2}=M^{2} L^{4} T^{-5} A^{-4}$
(iii) $[H]=\left[\frac{\text { Heat }}{\text { Mass }}\right]=\frac{M L^{2} T^{-2}}{M}=L^{2} T^{-2}$
(iv) $[s]=\left[\frac{\text { Heat }}{\text { Mass } \times \text { Temperature }}\right]$
$=\frac{M L^{2} T^{-2}}{M K}=L^{2} T^{-2} K^{-1}$