1

MCQ (More than One Correct Answer)
Using the expression $2d\sin \theta = \lambda$, one calculates the values of d by measuring the corresponding angles $\theta$ in the range 0 to 90o. The wavelength $\lambda$ is exactly known and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from 0o
A
the absolute error in d remains constant
B
the absolute error in d increases
C
the fractional error in d remains constant
D
the fractional error in d decreases
2

IIT-JEE 2010

MCQ (More than One Correct Answer)
A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?
A
Error ΔT in measuring T, the time period, is 0.05 seconds
B
Error ΔT in measuring T, the time period, is 1 second
C
Percentage error in the determination of g is 5%
D
Percentage error in the determination of g is 2.5%
3

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

4

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