Easy MCQ +4 / -1 PYQ · JEE Mains 2021

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

  1. A (a) $\to$ (iii), (b) $\to$ (ii), (c) $\to$ (iv), (d) $\to$ (i) Correct answer
  2. B (a) $\to$ (iii), (b) $\to$ (iv), (c) $\to$ (ii), (d) $\to$ (i)
  3. C (a) $\to$ (iv), (b) $\to$ (ii), (c) $\to$ (iii), (d) $\to$ (i)
  4. D (a) $\to$ (iv), (b) $\to$ (iii), (c) $\to$ (ii), (d) $\to$ (i)

Solution

q = CV<br><br>$[C] = \left[ {{q \over V}} \right] = {{(A \times T)} \over {M{L^2}{T^{ - 2}}}}$<br><br>$= {M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$<br><br>$[E] = \left[ {{F \over q}} \right] = {{ML{T^{ - 2}}} \over {AT}}$<br><br>$= ML{T^{ - 3}}{A^{ - 1}}$<br><br>$F = {{{q_1}{q_2}} \over {4\pi { \in _0}{r^2}}}$<br><br>$[{ \in _0}] = {M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$<br><br>Speed of light $c = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$<br><br>${\mu _0} = {1 \over {{ \in _0}{c^2}}}$<br><br>$[{\mu _0}] = {1 \over {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}]{{[L{T^{ - 1}}]}^2}}}$<br><br>$= [{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}]$

About this question

Subject: Physics · Chapter: Electrostatics · Topic: Electric Potential and Capacitance

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