Download App

Introduction to Physics — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsIntroduction to Physics5 Marks
Question
Test if the following equations are dimensionally correct:
  1. $\text{h}=\frac{2\text{S}\cos\theta}{\rho\text{rg}}$
  2. $\text{u}=\sqrt{\frac{\text{P}}{\rho}}$
  3. $\text{V}=\frac{\pi\text{Pr}^4\text{t}}{8\eta l}$
  4. $\text{v}=\frac{1}{2\pi}\sqrt{\frac{\text{mg}l}{\text{I}}}$
where h = height, S = surface tension, $\rho$ = density, P = pressure, V = volume, $\eta$ = coefficient of viscosity, v = frequency and I = moment of inertia.
✓

Answer

  1. $\text{h}=\frac{2\text{S}\cos\theta}{\rho\text{rg}}$
$\text{LHS}=[\text{L}]$

Surface tension $=\text{S}=\frac{\text{F}}{\text{I}}=\frac{\text{MLT}^{-2}}{\text{L}}=[\text{MT}^{-2}]$

Density $=\rho=\frac{\text{M}}{\text{V}}=[\text{ML}^{-3}\text{T}^{0}]$

Radius $=\text{r}=[\text{L],g = [LT}^{-2}]$

$\text{RHS}=\frac{2\text{S}\cos\theta}{\rho\text{rg}}=\frac{[\text{MT}^{-2}]}{[\text{ML}^{-3}\text{T}^0][\text{L}][\text{LT}^{-2}]}=[\text{M}^0\text{L}^1\text{T}^0]=[\text{L}]$

$\text{LHS = RHS}$

So, the relation is correct
  1. $\text{v}=\sqrt{\frac{\text{P}}{\rho}}$ where v = velocity
$\text{LHS = Dimension of v = [LT}^{-1}]$

Dimension of $\text{p}=\frac{\text{F}}{\text{A}}=[\text{ML}^{-1}\text{T}^{-2}]$

Dimension of $\rho=\frac{\text{m}}{\text{v}} = \text{[ML}^{-2}]$

$\text{RHS}=\sqrt{\frac{\text{p}}{\rho}}=\sqrt{\frac{[\text{ML}^{-1}\text{T}^{-2}]}{[\text{ML}^{-3}]}}=[\text{L}^2\text{T}^{-2}]^{\frac{1}{2}}=[\text{LT}^{-1}]$

So, the relation is correct.
  1. $\text{V}=\frac{(\pi\text{pr}^4\text{t})}{(8\eta\text{I})}$
$\text{LHS = Dimension of V = [L}^3]$

Dimension of $\text{p}=[\text{ML}^{-1}\text{T}^{-2}],\text{r}^4=[\text{L}^4],\text{t}=[\text{T}]$

Coefficient of viscosity $=[\text{ML}^{-1}\text{T}^{-1}]$

$\text{RHS}=\frac{\pi\text{pr}^4\text{t}}{8\eta\text{I}}=\frac{[\text{ML}^{-1}\text{T}^{-2}][\text{L}^4][\text{T}]}{[\text{ML}^{-1}\text{T}^{-1}][\text{L}]}$

So, the relation is correct.
  1. $\text{v}=\frac{1}{2\pi}\sqrt{(\text{mgI}/\text{I})}$
$\text{LHS = dimension of v = [T}^{-1}]$

$\text{RHS}=\sqrt{(\text{mgI}/\text{I})}=\sqrt{\frac{[\text{M}][\text{LT}^{-2}][\text{L}]}{[\text{ML}^2]}}=[\text{T}^{-1}]$

$\text{LHS = RHS}$

So, the relation is correct.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Introduction to Physics→Introduction to Physics — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$4 \times 10^{23}$ tritium atoms are contained in a vessel. The half-life of decay tritium nuclei is 12.3y. Find:
  1. The activity of the sample.
  2. The number of decay in the next 10 hours.
  3. The number of decays in the next 6.15y.
→
Two capacitors of capacitances 20.0pF and 50.0pF are connected in series with a 6.00V battery. Find:
  1. The potential difference across each capacitor.
  2. The energy stored in each capacitor.
→
Take $\text{C}_1=4.0\mu\text{F}$ and $\text{C}_2=6.0\mu\text{F}$ in figure. Calculate the equivalent capacitance of the combination between the points indicated.

→
A particle of mass m and charge q is thrown at a speed u against a uniform electric field E. How much distance will it travel before coming to momentary rest?
→
Explain ac voltage applied on a capacitor.Explain charging and discharging of a capacitor.
→
An electric field is uniform, and in the positive $x$ direction for positive $x$, and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E =200 \hat{ i } N / C$ for $x>0$ and $E =-200 \hat{ i } N / C$ for $x<0$. A right circular cylinder of length $20 \ cm$ and radius $5 \ cm$ has its centre at the origin and its axis along the $x-$ axis so that one face is at $x=+10 \ cm$ and the other is at $x=-10 \ cm\  ($Fig. $1.25).\ (a)$ What is the net outward flux through each flat face? $(b)$ What is the flux through the side of the cylinder? $(c)$ What is the net outward flux through the cylinder? $(d)$ What is the net charge inside the cylinder?
→
A U-shaped wire is placed before a concave mirror having radius of curvature 20cm. Find the total length of the image.
→
Suppose a 'n' - type wafer is created by doping Si crystal having $5 \times 10^{28} atoms/m^3$ with 1ppm concentration of As. On the surface 200 ppm Boron is added to create ‘P’ region in this wafer. Considering $n_i = 1.5 \times 10^{16}m^{-3}.$
  1. Calculate the densities of the charge carriers in the n & p regions.
  2. Comment which charge carriers would contribute largely for the reverse saturation current when diode is reverse biased.
→
Figure. shows a conductor of length l with a circular cross-section. The radius of the cross-section varies linearly from a to b. The resistivity of the material is ρ. Assuming that b - a << l, find the resistance of the conductor.
→
Consider an infinitely long wire carrying a current I (t), with $\frac{\text{dI}}{\text{dt}}=\lambda=\text{constant}$. Find the current produced in the rectangular loop of wire ABCD if its resistance is R (Fig).
→