Question 1 :
If {tex} Z = A ^ { 4 } B ^ { 1 / 3 } / C D ^ { 3 / 2 } , {/tex} than relative error in {tex} Z . \frac { \Delta Z } { Z } {/tex} is equal to
Question 2 :
Which of the following do not have the same dimensional formula as the velocity? Given that {tex} m _ { 0 } = {/tex} permeability of free space, {tex} e _ { 0 } = {/tex} permittivity of free space, {tex} n = {/tex} frequency, {tex} 1 = {/tex} wavelength, {tex} P = {/tex} pressure, {tex} r = {/tex} density, {tex} w = {/tex} angular frequency, {tex} k = {/tex} wave number,
Question 3 :
Surface tension of a liquid is 70 dyne/cm. Its value in SI is
Question 4 :
A physical quantity {tex}\mathrm A{/tex} is related to four observable quantities {tex}\mathrm a,b,c{/tex}and {tex}\mathrm d{/tex} as follows, A {tex} = \frac { a ^ { 2 } b ^ { 3 } } { c \sqrt { d } } {/tex} and the percentage errors of measurement in a, b, c and d are {tex} 1 \% , 3 \% , 2 \% {/tex} and {tex} 2 \% {/tex} respectively. What is the percentage error in the quantity {tex}\mathrm A{/tex}?
Question 6 :
Let {tex}\mathrm Q {/tex} denote the charge on the plate of a capacitor of capacitance {tex}\mathrm C . {/tex} The dimensional formula for {tex} \frac {\mathrm Q ^ { 2 } } { \mathrm C } {/tex} is
Question 7 :
Which of the following pairs of physical quantities does not have same dimensional formulae?
Question 8 :
Consider the following statements and select the correct option.<br>I. Every measurement by any measuring instrument has some error <br>II. Every calculated physical quantity that is based on measured values has some error <br>III. A measurement can have more accuracy but less precision and vice-versa.<br>
Question 9 :
The Richardson equation is given by {tex} \mathrm { I } = \mathrm { AT } ^ { 2 } \mathrm { e } ^ { - \mathrm { B } / \mathrm { kT } } . {/tex} The dimensional formula for {tex} \mathrm { AB } ^ { 2 } {/tex} is same as that for
Question 10 :
If velocity {tex} ( \mathrm { V } ) , {/tex} force {tex} ( \mathrm { F } ) {/tex} and energy {tex} ( \mathrm { E } ) {/tex} are taken as fundamental units, then dimensional formula for mass will be
Question 11 :
The moment of inertia of a body rotating about a given axis is {tex} 6.0 \mathrm { kg } \mathrm { m } ^ { 2 } {/tex} in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is {tex} 5 \mathrm { cm } {/tex} and the unit of mass is {tex} 10 \mathrm { g } {/tex} ?
Question 13 :
The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25 second. The percentage error in the measurement of time will be
Question 14 :
The refractive index of water measured by the relation {tex} \mathrm { m } = \frac { \text { real depth } } { \text { apparent depth } } {/tex} is found to have values of {tex} 1.34, 1.38, 1.32 {/tex} and {tex} 1.36 ; {/tex} the mean value of refractive index with percentage error is
Question 15 :
If {tex}\mathrm L{/tex} denotes the inductance of an inductor through which a current {tex}i{/tex} is flowing, the dimensions of {tex}\mathrm {Li^2}{/tex} are
Question 16 :
Resistance {tex} \mathrm { R } = \mathrm { V } / \mathrm { I } , {/tex} here {tex} \mathrm { V } = ( 100 \pm 5 ) \mathrm { V } {/tex} and {tex} \mathrm { I } = ( 10 \pm 0.2 ) \mathrm { A } . {/tex} Find percentage error in {tex} \mathrm { R } . {/tex}
Question 17 :
In the eqn. {tex} \left( P + \frac { a } { V ^ { 2 } } \right) ( V - b ) = {/tex} constant, the unit of a is
Question 19 :
A wire has a mass {tex} 0.3 \pm 0.003 \mathrm { g } {/tex}, radius {tex} 0.5 \pm 0.005 \mathrm { mm } {/tex} and length {tex} 6 \pm 0.06 \mathrm { cm } . {/tex} The maximum percentage error in the measurement of its density is
Question 20 :
{tex} \mathrm { A } , \mathrm { B } , \mathrm { C } {/tex} and {tex} \mathrm { D } {/tex} are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation {tex} \mathrm { AD } = \mathrm { C } \ln ( \mathrm { BD } ) {/tex} holds true. Then which of the combination is not a meaning ful quantity?
Question 21 :
{tex} \begin{array} { l l } { }{ \text { Column } \mathrm { I } } & { \text { Column } \mathrm { II } } \\ { \text { (A) Distance between earth and stars } } & { \text { (1) } \text { micron } } \\ { \text { (B) Inter-atomic distance in a solid } } & { \text { (2) angstrom } } \\ { \text { (C) Size of the nucleus } } & { \text { (3) } \mathrm { light\ year }} \\ { \text { (D)Wavelength of infrared laser } } & { \text { (4) fermi } }&\\&{ \text { (5) kilometre } } \end{array} {/tex}<br>
Question 23 :
The electric field is given by {tex} \vec { E } = \frac { A } { x ^ { 3 } } \hat { i } + B \hat { y } \hat { j } + C z ^ { 2 } \hat { k } . {/tex} The SI units of {tex}\mathrm {A, B}{/tex} and {tex} \mathrm { C } {/tex} are respectively: [where {tex} \mathrm { x } ,\mathrm y{/tex} and {tex}\mathrm z{/tex} are in {tex} \mathrm { m } ] {/tex}<br>
Question 24 :
In the equation {tex} \mathrm { P } = \frac { \mathrm { RT } } { \mathrm { V } - \mathrm { b } } \mathrm { e } ^ { \frac { \mathrm { aV } } { \mathrm { RT } } } {/tex} {tex} \mathrm { V } = {/tex} volume, {tex} \mathrm { P } = {/tex} pressure, {tex} \mathrm { R } = {/tex} universal gas constant, and {tex} \mathrm { T } = {/tex} temperature.
The dimensional formula of 'a' is same as that of
Question 25 :
If electronic charge {tex} \mathrm { e} {/tex}, electron mass {tex} \mathrm { m } , {/tex} speed of light in vacuum {tex} \mathrm { c } {/tex} and Planck's constant {tex} \mathrm { h } {/tex} are taken as fundamental quantities, the permeability of vacuum {tex} \mu _ { 0 } {/tex} can be expressed in units of
Question 26 :
In a new system of units, the fundamental quantities mass, length and time are replaced by acceleration {tex}'a', {/tex} density {tex}'\rho' {/tex} and frequency {tex} 'f' {/tex}. The dimensional formula for force in this system is
Question 27 :
If the dimensions of a physical quantity are given by {tex}\mathrm{ M ^ { a } L ^ { b } T ^ { c }}{/tex}, then the physical quantity will be
Question 28 :
A wire has a mass {tex} 0.3 \pm 0.003 {/tex} g, radius {tex} 0.5 \pm 0.005 {/tex} mm and length {tex} 6 \pm 0.06 \mathrm { cm } {/tex}. The maximum percentage error in the measurement of its density is
Question 30 :
Which one of the following is not measured in units of energy?
Question 31 :
Consider the following statements and select the correct statement(s).<br>{tex} \begin{array} { l l } { \text { I. } } & { 1 \text { calorie } = 4.18 \text { joule } } \\ { \text { II. } } & { 1 \mathrm { A } = 10 ^ { - 10 } \mathrm { m } } \\ { \text { III. } } & { 1 \mathrm { MeV } = 1.6 \times 10 ^ { - 13 } \mathrm { joule } } \\ { \mathrm { IV } . } & { 1 \text { newton } = 10 ^ { - 5 } \mathrm { dyne } } \end{array} {/tex}<br>
Question 32 :
{tex}\mathrm {Assertion :}{/tex} The time period of a pendulum is given by the formula, {tex}\mathrm{ T = 2 \pi \sqrt { \mathrm { g } / \ell } }{/tex}<br>{tex}\mathrm{ Reason :}{/tex} According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of {tex}\mathrm{L.H.S.}{/tex} is equal to dimensions of {tex}\mathrm{R.H.S.}{/tex}
Question 33 :
Which one of the following is not measured in units of energy?
Question 34 :
If {tex} \mathrm { v } = \frac { \mathrm { a } } { \mathrm { t } } + \mathrm { bt } ^ { 3 } {/tex} where {tex} \mathrm { v } = \mathrm { velocity } {/tex} and {tex} \mathrm { t } {/tex} is time The dimensional formula of {tex}\mathrm{a}{/tex} and {tex}\mathrm{b}{/tex} are
Question 35 :
The speed of light in vacuum, {tex} c , {/tex} depends on two fundamental constants, the permeability of free space, {tex} \mu _ { 0 } {/tex} and the permittivity of free space, {tex} \varepsilon _ { 0 } {/tex} The speed of light is given by {tex} c = \frac { 1 } { \sqrt { \mu _ { 0 } \varepsilon _ { 0 } } } . {/tex} The units of {tex} \varepsilon _ { 0 } {/tex} are {tex} \mathrm { N } ^ { - 1 } \mathrm { C } ^ { 2 } \mathrm { m } ^ { - 2 } {/tex}. The units for {tex} \mu _ { 0 } {/tex} are
Question 36 :
A spherical body of mass {tex} \mathrm { m } {/tex} and radius {tex}\mathrm r {/tex} is allowed to fall in a medium of viscosity {tex} \eta {/tex}. The time in which the velocity of the body increases from zero to {tex}0.63{/tex} times the terminal velocity {tex}\mathrm{(v)}{/tex} is called time constant {tex} ( \tau ) . {/tex} Dimensionally {tex} \tau {/tex} can be represented by :
Question 37 :
The dimensions of {tex} \frac { 1 } { \epsilon _ { \mathrm { o } } } \frac { \mathrm { e } ^ { 2 } } { \mathrm { hc } } {/tex} are
Question 38 :
Which one of the following is not a unit of Young’s modulus?
Question 39 :
The unit of the coefficient of viscosity in S.I. system is
Question 40 :
The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends){tex}^n{/tex} and (average velocity of the liquid){tex}^m{/tex} . Which of the following relations between {tex} \mathrm { m } {/tex} and {tex} \mathrm { n } {/tex} is correct?
Question 41 :
In a vernier callipers, ten smallest divisions of the vernier scale are equal to nine smallest division on the main scale. If the smallest division on the main scale is half millimeter, then the vernier constant is
Question 42 :
A physical quantity {tex} \zeta {/tex} is calulated using the formula {tex} \zeta = \frac { 1 } { 10 } x y ^ { 2 } / z ^ { 1 / 3 } , {/tex} where {tex} x , y {/tex} and {tex} z {/tex} are experimentally measured quantities. If the fractional error in the measurement of {tex} x , y {/tex} and {tex} z {/tex} are {tex} 2 \% , 1 \% {/tex} and {tex} 3 \% {/tex} respectively, then the fractional error in {tex} \zeta {/tex} will be<br>
Question 45 :
The length of one rod {tex} \ell _ { 1 } = 3.323 \mathrm { cm } {/tex} and the other is {tex} \ell _ { 2 } = 3.321 \mathrm { cm } . {/tex} Both rods were measured with one measuring instrument with least count {tex} 0.001 \mathrm { cm } {/tex} Then {tex} \left( \ell _ { 1 } - \ell _ { 2 } \right) {/tex} is
