Units and Dimensions

Relative error is unitless and dimensionless. Absolute error has dimension.

Least count = $\frac{Pitch}{No. of circular scale divisions}$ ∴ Statement I is false.
Statement II is true because smaller pitch means, smaller least count. ∴ Greater accuracy.

[Stress] = [Modulus of Elasticity] = [Pressure]
= [Energy density] = $[ML^{-1}T^{-2}]$ [Strain] = [Angle] = $[M^{0}L^{0}T^{0}]$ [Torque] = [Energy] = $[ML^{2}T^{-2}]$

Electrical resistance [Use P = I²R] $R = \frac{[P]}{[I^{2}]} = \frac{[ML^{2}T^{-3}]}{[A^{2}]} = [ML^{2}T^{-3}A^{-2}]$ Capacitance $\left[\text{use } U=\frac{1}{2}\frac{Q^{2}}{C}\right]$ $[C]=\frac{[Q^{2}]}{[U]}=\frac{[AT]^{2}}{[ML^{2}T^{-2}]}=[M^{-1}L^{-2}T^{4}A^{2}]$
Magnetic field [use F = ILB]
$[ \mathrm{B} ] = \frac {[ \mathrm{F} ]}{[ \mathrm{I} ] [ \mathrm{L} ]} = \frac {[ \mathrm{MLT} ^ {- 2} ]}{[ \mathrm{A} ] [ \mathrm{L} ]} = [ \mathrm{MT} ^ {- 2} \mathrm{A} ^ {- 1} ]$
Inductance [use U = $\frac{1}{2}$ LI $^{2}$ ]
$[ \mathrm{L} ] = \frac {[ \mathrm{U} ]}{[ \mathrm{I} ] ^ {2}} = \frac {[ \mathrm{ML} ^ {2} \mathrm{T} ^ {- 2} ]}{[ \mathrm{A} ^ {2} ]} = [ \mathrm{ML} ^ {2} \mathrm{T} ^ {- 2} \mathrm{A} ^ {- 2} ]$

Boltzmann constant (use $E = \frac{3}{2} K T$ )
$[ \mathrm{K} ] = \mathrm{ML} ^ {2} \mathrm{T} ^ {- 2} \mathrm{K} ^ {- 1}$
Coefficient of viscosity (use $\eta=\frac{F}{A}\left(\frac{\Delta x}{\Delta v}\right)$ )
$[ \eta ] = [ \mathrm{ML} ^ {- 1} \mathrm{T} ^ {- 1} ]$
Planck's constant (use E = hv)
$[ \mathrm{h} ] = [ \mathrm{ML} ^ {2} \mathrm{T} ^ {- 1} ]$
Thermal conductivity (use $K=\frac{i_{t}L}{A\Delta\theta}$ )
$[ \mathrm{K} ] = [ \mathrm{MLT} ^ {- 3} \mathrm{K} ^ {- 1} ]$

[Energy density] = [Young's modulus] = $[ML^{-1}T^{-2}]$

[h] = [Angular impulse] = [Angular momentum]
= $[ML^{2}T^{-1}]$

D

A

A