Units and Measurement

Bonus $\mathrm{}V=K\left(h{)}^a\right(I{)}^b\left(G{)}^c\right(C{)}^d\mathrm{}(V$

is voltage   $)$ $$

We know,   $\begin{array}{rr}& \left[\mathrm{h}\right]={\mathrm{M}\mathrm{L}}^2{\mathrm{T}}^{-1}\\ & \left[\mathrm{l}\right]=\mathrm{A}\\ & \left[\mathrm{G}\right]={\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\\ & \left[\mathrm{C}\right]=\mathrm{L}{\mathrm{T}}^{-1}\\ & \left[\mathrm{V}\right]=\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\end{array}$

$M{L}^2{T}^{-3}{A}^{-1}={\left(M{L}^2{T}^{-1}\right)}^a(A{)}^b{\left(M^{-1}{L}^3{T}^{-2}\right)}^c{\left(L{T}^{-1}\right)}^d$

$M{L}^2{T}^{-3}{A}^{-1}=M^{a-c}{L}^{2a+3c+d}{T}^{-a-2c-d}{A}^b$

$\mathrm{a}-\mathrm{c}=1$

$2\mathrm{a}+3\mathrm{c}+\mathrm{d}=2$

$-a-2c-d=-3$

$b=-1$

On solving,

$c=-1$ $a=0$

$\mathrm{d}=5,\mathrm{b}=-1$

$V=K\left(h{)}^{?}\right(I{)}^{-1}\left(G{)}^{-1}\right(C{)}^5$

Magnetic energy per unit volume $=\frac{{\mathrm{B}}^2}{2{\mu }_0}$

Kindly consider the following Image

Kindly consider the following Image

using hook's law:
σ = Yε ⇒ f/A = Y (x/l) ⇒ Y = fl/ (xA) = fl/ (xπr²)
Using error analysis formula:
ΔY/Y = Δf/f + Δl/l + Δx/x + 2Δr/r
%error in Y = [ (Δm/m) + (Δl/l) + (Δx/x) + 2 (Δr/r) ] * 100
= [ (1/1000) + (1/1000) + (0.001/0.5) + 2 (0.001/0.2) ] * 100
= [ 0.001 + 0.001 + 0.002 + 0.01 ] * 100 = 1.4%

Δy/y = 2Δm/m + 4Δr/r + |x|Δg/g + (3/2)Δl/l
18 = 2 (1) + 4 (0.5) + |x|p + (3/2)4
18 = 2 + 2 + |x|p + 6 = 10 + |x|p
8 = |x|p
From the options, if x=8, p=±1. If x=16/3, p=±3/2. If x=5, p=±8/5. If x=4, p=±2.
Option B gives x=16/3, and p is not among the options.
Option A gives x=5, p not among options.
Option C gives x=8, p not among options.
Option D gives x=4, p not among options.
There must be a typo in the question or options. The solution gives x=16/3 and p=3/2. Let's check.
8 = (16/3) * (3/2) = 8. So B is correct.

[C] = Q/V = Q/ (W/Q) = Q²/W = (A²T²)/ (M¹L²T? ²) = M? ¹L? ²T? A²
[ε? ] = C/ (4πr²) * (Fr²/q²) = M? ¹L? ³T? A²
[µ? ] = 4πrF/I²l = M¹L¹T? ²A? ²
[E] = F/q = (MLT? ²)/ (AT) = MLT? ³A? ¹

Difference in Reading = Positive Zero Error - Negative Zero Error
= (+5) - [- (100-92)]
= 5 - [-8]
= 13

Least count = Pitch / (Total divisions on circular scale)
In 5 revolution, distance travelled = 5mm
? In 1 revolution, distance travelled = 1mm
So least count = 1/50 = 0.02mm = 0.002 cm
So, Assertion is not correct but reason is correct

Dimension of B = [L? ¹]
Dimension of D = [T? ¹]
Dimension of A = [MLT? ²]
The dimensional formula of AD/B
= [MLT? ²] [T? ¹]/ [L? ¹] = [ML²T? ³]