Match List-I with List-II. List-I List-II (a) Capacitance, C (i) M 1 L 1 T -3 A -1 (b) Permittivity of free space, 0 (ii) M -1 L -3 T 4 A 2 (c) Permeability of free space, μ0 (iii) M -1 L-2 T4 A2 (d) Electric field, E (iv) M 1 L 1 T -2 A -2 Choose the correct answer from the options given below

(B) (a) \rightarrow(i i i),(b) \rightarrow(i v),(c) \rightarrow(i i),(d) \rightarrow(i)

(C) (a) \rightarrow(iv),(b) \rightarrow(i i),(c) \rightarrow(iii),(d) \rightarrow(i)

(D) (a) \rightarrow(iv),(b) \rightarrow(iii),(c) \rightarrow(ii),(d) \rightarrow(i)

JEE Mains · Physics · STD 11 - Units,dimensions and measurement

Match List\(-I\) with List\(-II.\)

List\(-I\) List\(-II\)

\((a)\) Capacitance, \(C\) \((i)\) \({M}^{1} {L}^{1} {T}^{-3} {A}^{-1}\)

\((b)\) Permittivity of free space, \(\varepsilon_{0}\) \((ii)\) \({M}^{-1} {L}^{-3} {T}^{4} {A}^{2}\)

\((c)\) Permeability of free space, \(\mu_{0}\) \((iii)\) \({M}^{-1} L^{-2} T^{4} A^{2}\)

\((d)\) Electric field, \(E\) \((iv)\) \({M}^{1} {L}^{1} {T}^{-2} {A}^{-2}\)

Choose the correct answer from the options given below

Pick an option to check your answer.

Verified Solution

Correct Answer

(A) \((a) \rightarrow(i i i),(b) \rightarrow(i i),(c) \rightarrow(i v),(d) \rightarrow(i)\)

Detailed explanation

As we know

\(q=C V\)

\({[C]=\left[\frac{q}{V}\right]=\frac{(A \times T)^{2}}{M L^{2} T^{-2}}}\)

\(=M^{-1} L^{-2} T^{4} A^{2}\)

\({[E]=\left[\frac{F}{q}\right]=\frac{M L T^{-2}}{A T}}\)

\(=M L T_{q}^{-3} A^{-1}\)

\(F=\frac{q_{1} q_{2}}{4 \pi \epsilon_{0} r^{2}}\)

\({\left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{4} A^{2}}\)

\(\text { Speed of light } c=\frac{1}{\sqrt{\mu_{0} \in_{0}}}\)

\(\mu_{0}=\frac{1}{\epsilon_{0} c^{2}}\)

\({\left[\mu_{0}\right]=\frac{1}{\left[M^{-1} L^{-3} T^{4} A^{2}\right]\left[L T^{-1}\right]^{2}}}\)

\(=\left[M^{1} L^{1} T^{-2} A^{-2}\right]\)

Same subject

From JEE Mains

List\(-I\)	List\(-II\)
\((a)\) Capacitance, \(C\)	\((i)\) \({M}^{1} {L}^{1} {T}^{-3} {A}^{-1}\)
\((b)\) Permittivity of free space, \(\varepsilon_{0}\)	\((ii)\) \({M}^{-1} {L}^{-3} {T}^{4} {A}^{2}\)
\((c)\) Permeability of free space, \(\mu_{0}\)	\((iii)\) \({M}^{-1} L^{-2} T^{4} A^{2}\)
\((d)\) Electric field, \(E\)	\((iv)\) \({M}^{1} {L}^{1} {T}^{-2} {A}^{-2}\)