1

IIT-JEE 1998

MCQ (More than One Correct Answer)
Let [${\mathrm\varepsilon}_\mathrm o$] denote the dimentional formula of the permittivity of the vacuum, and [$\mu_o$] that of the permeability of the vacuum.If M = mass, L = length, T = time and I = electric current,
A
$\left[{\mathrm\varepsilon}_\mathrm o\right]\;=\;\mathrm M^{-1}\mathrm L^{-3}\mathrm T^2\;\mathrm I$
B
$\left[{\mathrm\varepsilon}_\mathrm o\right]\;=\;\mathrm M^{-1}\mathrm L^{-3}\mathrm T^4\mathrm I^2$
C
$\left[{\mathrm\mu}_\mathrm o\right]\;=\;\mathrm{MLT}^{-2}\mathrm I^{-2}$
D
$\left[{\mathrm\mu}_\mathrm o\right]\;=\;\mathrm{ML}^2\mathrm T^{-1}\;\mathrm I$

Explanation

From coulombs law, we know that

$F = {1 \over {4\pi {\varepsilon _0}}}{{{q_1}{q_2}} \over {{r^2}}} \Rightarrow {\varepsilon _0} = {1 \over {4\pi }}{{{q_1}{q_2}} \over {{r^2}F}}$

Therefore, ${\varepsilon _0} = {{[{I^2}{T^2}]} \over {[{L^2}][ML{T^{ - 2}}]}} = {M^{ - 1}}{L^{ - 3}}{T^4}{I^2}$

Now, $c = {1 \over {\sqrt {{\varepsilon _0}{\mu _0}} }} \Rightarrow {c^2} = {1 \over {{\varepsilon _0}{\mu _0}}}$

Therefore, ${\mu _0} = {1 \over {{c^2}{\varepsilon _0}}} = {1 \over {{{[L{T^{ - 1}}]}^2}[{M^{ - 1}}{L^{ - 3}}{T^4}{I^2}]}} = [ML{T^{ - 2}}{I^{ - 2}}]$

2

IIT-JEE 1998

MCQ (More than One Correct Answer)
The SI unit of inductance, the henry can be written as
A
weber/ampere
B
volt-sec/amp
C
Joule/(ampere)2
D
ohm-second

Explanation

Induction $L = {\phi \over i} =$ weber/Ampere

Also, $e = - L\left( {{{di} \over {dt}}} \right) \Rightarrow L = {{ - e} \over {(di/dt)}} = {{volt - {\mathop{\rm second}\nolimits} } \over {Ampere}}$

Also, $U = {1 \over 2}L{i^2} \Rightarrow L = {{2U} \over {{i^2}}} = {{Joule} \over {{{(Ampere)}^2}}}$

and $U = {1 \over 2}L{i^2} = {i^2}RT \Rightarrow L = RT =$ Ohm-second

3

IIT-JEE 1995 Screening

MCQ (More than One Correct Answer)
The pairs of physical quantities that have the same dimensions is (are):
A
Reynolds number and coefficient of friction
B
Curie and frequency of a light wave
C
Latent heat and gravitational potential
D
Planck's constant and torque
4

IIT-JEE 1986

MCQ (More than One Correct Answer)
The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)
A
Torque and Work
B
Angular momentum and Work
C
Energy and Young's modulus
D
Light year and Wavelength