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The dimensional formula of the coefficient of thermal conductivity is :
1.  $\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-3}{\mathrm{K}}^{-1}\right]$
2.  $\left[{\mathrm{M}}^3{\mathrm{L}}^{-1}{\mathrm{T}}^{-3}\mathrm{K}\right]$
3.  $\left[{\mathrm{M}}^1{\mathrm{L}}^{-3}{\mathrm{T}}^{-1}{\mathrm{K}}^{-1}\right]$
4.  $\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-3}\mathrm{K}\right]$

If L,Q,R represent inductance, charge and resistance respectively, the units of 
[This question includes concepts from 12th syllabus]
1. $\frac{QR}{L}$ will be those of current
2. $\frac{Q^2{R}^3}{L^2}$ will be those of energy
3. $\frac{QL}{R}$ will be those of current
4. $\frac{Q^3{R}^2}{L}$ will be those of power                   

Which of the following is not equal to a watt?
1. Joule/second
2. Ampere\(\times\) volt
3. ( Ampere)²\(\times\) ohm
4. Ampere/volt

Which of the following is not represented in correct unit  
(1) $\frac{\text{Stress}}{\text{Strain}}=N\text{}/\text{}{m}^2$
(2) Surface tension = $N\text{}/\text{}m$
(3) Energy $=kg\text{-}m\text{}/\text{}\sec$
(4) Pressure $=N\text{}/\text{}{m}^2$

SI unit of pressure is
(1) Pascal
(2) $Dynes/c{m}^2$
(3) cm of Hg
(4) Atmosphere

In $$\(S= a+bt+ct^2,~S\) is measured in metres and \(t\) in seconds. The unit of \(c\) will be:

The density of wood is $0.5gm/cc$ in the CGS system of units. The corresponding value in MKS units is :
(1) 500
(2) 5
(3) 0.5
(4) 5000

If the unit of length and force be increased four times, then the unit of energy is 
1. Increased 4 times
2. Increased 8 times
3. Increased 16 times
4. Decreased 16 times

If \(u_1\) and \(u_2\) are the units selected in two systems of measurement and \(n_1\) and \(n_2\) are their numerical values, then:

1 eV is 
(1) Same as one joule
(2) $1.6\times {10}^{-19}J$
(3) 1 V
(4) $1.6\times {10}^{-19}C$

To determine Young's modulus of a wire, the formula is $Y=\frac{F}{A}\times \frac{L}{\Delta L};$ where L = length, A = area of cross-section of the wire, $\Delta L=$change in length of the wire when stretched with a force F. The conversion factor to change it from CGS to MKS system is
(1) 1
(2) 10
(3) 0.1
(4) 0.01

[This question includes concepts from 12th syllabus] 
Codes:                                                                                        
(1) $I-A,II-F,III-E,IV-D$
(2) $I-C,II-F,III-A,IV-B$
(3) $I-C,II-F,III-A,IV-E$
(4) $I-B,II-F,III-A,IV-C$

Given the equation \(\left(P+\frac{a}{V^2}\right)(V-b)=\text {constant}\). The units of \(a\) will be: (where \(P\) is pressure and \(V\) is volume)
1. \(\text{dyne} \times \text{cm}^5\)
2. \(\text{dyne} \times \text{cm}^4\)
3. \(\text{dyne} / \text{cm}^3\)
4. \(\text{dyne} / \text{cm}^2\)

In C.G.S. system the magnitutde of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is
(1) 0.036
(2) 0.36
(3) 3.6
(4) 36

The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type $f=C{m}^x{K}^y$; where C is a dimensionless quantity. The value of x and y are 
1. $x=\frac{1}{2},y=\frac{1}{2}$
2. $x=-\frac{1}{2},y=-\frac{1}{2}$
3. $x=\frac{1}{2},y=-\frac{1}{2}$
4. $x=-\frac{1}{2},y=\frac{1}{2}$

The velocity of water waves v may depend upon their wavelength $\lambda$, the density of water $\rho$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as: 
1. ${\mathrm{v}}^2\propto {\mathrm{g\lambda }}^{-1}{\mathrm{\rho }}^{-1}$
2. ${\mathrm{v}}^2\propto \mathrm{g\lambda \rho }$
3. ${\mathrm{v}}^2\propto \mathrm{g\lambda }$
4. ${\mathrm{v}}^2\propto {\mathrm{g}}^{-1}{\mathrm{\lambda }}^{-3}$

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on (i) the mass of the ball m, (ii) $\eta$, (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct?
1. $v_T\propto \frac{mg}{\eta r}$
2. $v_T\propto \frac{\eta r}{mg}$
3. $v_T\propto \eta rmg$
4. $v_T\propto \frac{mgr}{\eta }$ 

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^2}{4\pi {\epsilon }_o}$ is [c is the velocity of light, G is the universal constant of gravitation and e is charge]
(a) $\frac{1}{c^2}{\left[G\frac{e^2}{4\pi {\epsilon }_o}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
(b) $c^2{\left[G\frac{e^2}{4\pi {\epsilon }_o}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
(c) $\frac{1}{c^2}{\left[\frac{e^2}{G4\pi {\epsilon }_o}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
(d) $\frac{1}{c}G\frac{e^2}{4\pi {\epsilon }_0}$

If dimensions of critical velocity v_c of a liquid flowing through a tube are expressed as [$\eta$^xρ^yr^z]  , where $\eta$, ρ and r are the coefficient of viscosity of the liquid, the density of liquid and radius of the tube respectively, then the values of x,y and z are given by
1. 1, -1, -1
2. -1, -1, 1
3. -1, -1, -1
4. 1, 1, 1

The density of material in the CGS system of units is $4g/c{m}^3.$ In a system of units in which unit of length is 10cm and unit of mass is 100g when the value of density of material in this system will be:
(1) 0.4
(2) 40
(3) 400
(4) 0.04 

 
Which two of the following five physical parameters have the same dimensions ?
(1) energy density 
(2) refractive index 
(3) dielectric constant 
(4) Young's modulus 
(5) magnetic field 
1. 2 and 4
2. 3 and 5 
3. 1 and 4 
4. 1 and 5