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1.Units, Dimensions and Measurement
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લિસ્ટ $-I$ ને લિસ્ટ $-II$ સાથે સરખાવો
| લિસ્ટ $-I$ | લિસ્ટ $-II$ |
| $(a)$ કેપેસીટન્સ, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
| $(b)$ શૂન્યાવકાશની પરમિટિવિટી, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
| $(c)$ શૂન્યાવકાશની પરમીએબીલીટી, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
| $(d)$ વિદ્યુતક્ષેત્ર, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
A$(a) \rightarrow(i i i),(b) \rightarrow(i i),(c) \rightarrow(i v),(d) \rightarrow(i)$
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 MAIN-2021)
Solution
As we know
$q=C V$
${[C]=\left[\frac{q}{V}\right]=\frac{(A \times T)^{2}}{M L^{2} T^{-2}}}$
$=M^{-1} L^{-2} T^{4} A^{2}$
${[E]=\left[\frac{F}{q}\right]=\frac{M L T^{-2}}{A T}}$
$=M L T_{q}^{-3} A^{-1}$
$F=\frac{q_{1} q_{2}}{4 \pi \epsilon_{0} r^{2}}$
${\left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{4} A^{2}}$
$\text { Speed of light } c=\frac{1}{\sqrt{\mu_{0} \in_{0}}}$
$\mu_{0}=\frac{1}{\epsilon_{0} c^{2}}$
${\left[\mu_{0}\right]=\frac{1}{\left[M^{-1} L^{-3} T^{4} A^{2}\right]\left[L T^{-1}\right]^{2}}}$
$=\left[M^{1} L^{1} T^{-2} A^{-2}\right]$
$q=C V$
${[C]=\left[\frac{q}{V}\right]=\frac{(A \times T)^{2}}{M L^{2} T^{-2}}}$
$=M^{-1} L^{-2} T^{4} A^{2}$
${[E]=\left[\frac{F}{q}\right]=\frac{M L T^{-2}}{A T}}$
$=M L T_{q}^{-3} A^{-1}$
$F=\frac{q_{1} q_{2}}{4 \pi \epsilon_{0} r^{2}}$
${\left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{4} A^{2}}$
$\text { Speed of light } c=\frac{1}{\sqrt{\mu_{0} \in_{0}}}$
$\mu_{0}=\frac{1}{\epsilon_{0} c^{2}}$
${\left[\mu_{0}\right]=\frac{1}{\left[M^{-1} L^{-3} T^{4} A^{2}\right]\left[L T^{-1}\right]^{2}}}$
$=\left[M^{1} L^{1} T^{-2} A^{-2}\right]$
Standard 11
Physics
Similar Questions
લીસ્ટ $I$ સાથે લીસ્ટ $II$ યોગ્ય રીતે જોડો.
| લીસ્ટ $I$ (ભૌતિક રાશી) | લીસ્ટ $II$ (પારિમાણિક સૂત્ર) |
| $(A)$ દબાણ પ્રચલન | $(I)$ $\left[ M ^0 L ^2 T ^{-2}\right]$ |
| $(B)$ ઊર્જા-ઘનતા | $(II)$ $\left[ M ^1 L ^{-1} T ^{-2}\right]$ |
| $(C)$ વિદ્યુતક્ષેત્ર | $(III)$ $\left[ M ^1 L ^{-2} T ^{-2}\right]$ |
| $(D)$ ગુપ્ત ઉષ્મા | $(IV)$ $\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$ |
