Question 1 :
If {tex} \mathrm { L } = 2.331 \mathrm { cm } , \mathrm { B } = 2.1 \mathrm { cm } , {/tex} then {tex} \mathrm { L } + \mathrm { B } = {/tex}
Question 2 :
The physical quantity which has the dimensional formula {tex} \left[ \mathrm { M } ^ { 1 } \mathrm { T } ^ { - 3 } \right] {/tex} is
Question 3 :
If {tex} Q {/tex} denote the charge on the plate of a capacitor of capacitance {tex} C {/tex} then the dimensional formula for {tex} \frac { Q ^ { 2 } } { C } {/tex} is
Question 6 :
In the relation {tex} x = \cos ( \omega t + k x ) , {/tex} the dimension(s) of {tex} \omega {/tex} is/are
Question 11 :
The values of kinetic energy {tex} \mathrm { K } {/tex} and potential energy {tex} \mathrm { U } {/tex} are measured as follows: {tex} \mathrm { K } = 100.0 \pm 2.0 \mathrm { J } , \mathrm { U } = 200.0 \pm 1.0 \mathrm { J } . {/tex} Then the percentage error in the measurement of mechanical energy is -
Question 13 :
Number of significant figures in expression {tex} \frac { 4.327 \mathrm { g } } { 2.51 \mathrm { cm } ^ { 3 } } {/tex} is<br>
Question 14 :
What is the correct number of significant figures in {tex} 0.0003026 ? {/tex}
Question 15 :
If unit of length and force are increased {tex}4{/tex} times. The unit of energy
Question 16 :
If {tex} Z = A ^ { 3 } , {/tex} then {tex} \frac { \Delta Z } { Z } = {/tex}
Question 17 :
A thin copper wire of length {tex} l {/tex} metre increases in length by {tex} 2 \% {/tex} when heated through {tex} 10 ^ { \circ } \mathrm { C } {/tex}. What is the percentage increase in area when a square copper sheet of length {tex} l {/tex} metre is heated through {tex} 10 ^ { \circ } \mathrm { C } ? {/tex}
Question 18 :
The pitch and the number of circular scale divisions in a screw gauge with least count {tex} 0.02 \mathrm { mm } {/tex} are respectively
Question 19 :
The pitch of the screw gauge is {tex} 0.5 \mathrm { mm } {/tex}. Its circular scale contains {tex}50{/tex} divisions. The least count of the screw gauge is
Question 20 :
In equation, {tex} \mathrm { r } = \mathrm { m } ^ { 2 } \sin \pi \mathrm { t } , {/tex} where t represents time. If the unit of {tex} \mathrm { m } {/tex} is {tex} \mathrm { N } {/tex}, then the unit of {tex} \mathrm { r } {/tex} is
Question 21 :
Distance travelled by a particle at any instant {tex}\mathrm{'t'}{/tex} can be represented as {tex}\mathrm{ S = A ( t + B ) + C t ^ { 2 }} . {/tex} The dimensions of {tex}\mathrm{B}{/tex} are
Question 22 :
If {tex}\mathrm L = 2.331 \mathrm { cm } ,\mathrm B = 2.1 \mathrm { cm } , {/tex} then {tex} \mathrm { L } + \mathrm { B } = {/tex}
Question 23 :
In the eqn. {tex} \left( \mathrm { P } + \frac { \mathrm { a } } { \mathrm { V } ^ { 2 } } \right) ( \mathrm { V } - \mathrm { b } ) = {/tex} constant, the unit of {tex}\mathrm{a}{/tex} is
Question 24 :
Which one of the following represents the correct dimensions of the gravitational constant?
Question 25 :
Young's modulus of steel is {tex} 1.9 \times 10 ^ { \mathrm { 11 } } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex} When expressed in CGS units of dyne/cm {tex} ^ { 2 } {/tex}, it will be equal to {tex} \left( 1 \mathrm { N } = 10 ^ { 5 } \mathrm { dyne } , 1 \mathrm { m } ^ { 2 } = 10 ^ { 4 } \mathrm { cm } ^ { 2 } \right) {/tex}
Question 26 :
Error in the measurement of radius of a sphere is {tex} 1 \% . {/tex} Then error in the measurement of volume is
Question 27 :
A boy recalls the relation almost correctly but forgets where to put the constant {tex} c {/tex} (speed of light). He writes; {tex} m = \frac { m _ { 0 } } { \sqrt { 1 - v ^ { 2 } } } , {/tex} where mand {tex} m _ { 0 } {/tex} stand for masses and {tex} v {/tex} for speed. Right place of {tex} c {/tex} is
Question 28 :
Let {tex} Q {/tex} denote the charge on the plate of a capacitor of capacitance {tex} C . {/tex} The dimensional formula for {tex} \frac { Q ^ { 2 } } { C } {/tex} is
Question 30 :
The quantity having the same units in all systems of units is
Question 31 :
The division of energy by time is {tex} \mathrm { X } . {/tex} The dimensional formula of {tex} \mathrm { X } {/tex} is same as that of
Question 32 :
Which one of the following represents the correct dimensions of the coefficient of viscosity?
Question 33 :
The heat generated in a circuit is given by {tex} Q = I ^ { 2 }Rt {/tex} , where {tex} \mathrm I {/tex} is current, {tex} R {/tex} is resistance and {tex} \mathrm t {/tex} is time. If the percentage errors in measuring {tex}I, R {/tex} and t are {tex} 2 \% , 1 \% {/tex} and {tex} 1 \% {/tex} respectively, then the maximum error in measuring heat will be
Question 36 :
{tex} \left[ \mathrm { MLT } ^ { - 1 } \right] + \left[ \mathrm { MLT } ^ { - 1 } \right] = \ldots \ldots \ldots \ldots {/tex}
Question 37 :
What are the dimensions of {tex} \mathrm { A } / \mathrm { B } {/tex} in the relation {tex} \mathrm { F } = \mathrm { A } \sqrt { \mathrm { x } } + \mathrm { Bt } ^ { 2 } , {/tex} where {tex}\mathrm F {/tex} is the force, {tex} x {/tex} is the distance and {tex} t {/tex} is time?
Question 39 :
In a simple pendulum experiment, the maximum percentage error in the measurement of length is {tex} 2 \% {/tex} and that in the observation of the time- period is {tex} 3 \% . {/tex} Then the maximum percentage error in determination of the acceleration due to gravity g is
Question 40 :
If {tex} x = a t + b t ^ { 2 } , {/tex} where {tex} x {/tex} is the distance travelled by the body in kilometers while {tex} t {/tex} is the time in seconds, then the unit of {tex} b {/tex} is
Question 43 :
Which of the following physical quantities has neither dimensions nor unit?
Question 46 :
The thrust developed by a rocket-motor is given by {tex} \mathrm { F } = \mathrm { mv } + \mathrm { A } \left( \mathrm { P } _ { 1 } - \mathrm { P } _ { 2 } \right) {/tex} where {tex} \mathrm { m } {/tex} is the mass of the gas ejected per unit time, {tex}\mathrm v{/tex} is velocity of the gas, {tex} \mathrm { A } {/tex} is area of cross-section of the nozzle, {tex} \mathrm { P } _ { 1 } {/tex} and {tex} \mathrm { P } _ { 2 } {/tex} are the pressures of the exhaust gas and surrounding atmosphere. The formula is dimensionally
Question 47 :
The resistance {tex} R {/tex} of a wire is given by the relation {tex} R = \frac { \rho \ell } { \pi r ^ { 2 } } . {/tex} Percentage error in the measurement of {tex} \rho , \ell {/tex} and {tex} r {/tex} is {tex} 1 \% , 2 \% {/tex} and {tex} 3 \% {/tex} respectively. Then the percentage error in the measurement of {tex} R {/tex} is
Question 49 :
{tex} \mathrm { E } , \mathrm { m } , \mathrm { J } {/tex} and {tex} \mathrm { G } {/tex} denote energy, mass, angular momentum and gravitational constant respectively, then the unit of {tex} \frac { \mathrm { E } \mathrm { J } ^ { 2 } } { \mathrm { m } ^ { 5 } \mathrm { G } ^ { 2 } } {/tex} is
Question 51 :
If force (F), length (L) and time (T) assumed to be fundamental units, then the dimensional formula of the mass will be
Question 53 :
In a vernier callipers {tex} N {/tex} division of vernier coincide with {tex} ( N - 1 ) {/tex} divisions of main scale in which length of a division is {tex} 1 \mathrm { mm } {/tex}. The least count of the instrument in {tex} \mathrm { cm } {/tex} is
Question 54 :
Write the dimensions of {tex}\mathrm{a \times b }{/tex} in the relation {tex} \mathrm{E = \frac { b - x ^ { 2 } } { a t }} {/tex}, where {tex} \mathrm { E } {/tex} is the energy, {tex} x {/tex} is the displacement and t is time
Question 55 :
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 56 :
{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 57 :
One centimetre on the main scale of a vernier callipers is divided into {tex}10{/tex} equal parts. If {tex}10{/tex} divisions of vernier coincide with {tex}8{/tex} small divisions of the main scale, the least count of vernier callipers is
Question 58 :
Area of a square is {tex} ( 100 \pm 2 ) \mathrm { m } ^ { 2 } . {/tex} Its side is
Question 59 :
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 60 :
The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimensions of
Question 61 :
A physical quantity {tex} x {/tex} depends on quantities {tex} y {/tex} and {tex} z {/tex} as follows: {tex} x = A y + B \tan C z , {/tex} where {tex} A , B {/tex} and {tex} C {/tex} are constants. Which of the following do not have the same dimensions:
Question 62 :
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 63 :
The density of a sphere is measured by measuring its mass and diameter. If, it is known that the maximum percentage errors in the measurement are {tex} 2 \% {/tex} and {tex} 3 \% , {/tex} then find the maximum percentage error in the measurement of density?
Question 65 :
Two masses {tex} \mathrm { M } _ { \mathrm { A } } {/tex} and {tex} \mathrm { M } _ { \mathrm { B } } \left( \mathrm { M } _ { \mathrm { A } } < \mathrm { M } _ { \mathrm { B } } \right) {/tex} are weighed using same weighing machine. Absolute error and relative error in two measurement are (Assume only systematic errors are nvolved)
Question 66 :
If the dimensions of a physical quantity are given by {tex} \mathrm { M } ^ { \mathrm { a } } \mathrm { L } ^ { \mathrm { b } } \mathrm { T } ^ { \mathrm { c } } , {/tex} then the physical quantity will be
Question 67 :
The refractive index of water measured by the relation {tex} \mu = \frac { \text { real depth } } { \text { apparent } } {/tex} is found to have values of 1.34, 1.38, 1.32 and 1.36, the mean value of refractive index with perfentage error is
Question 68 :
In an experiment four quantities {tex}\mathrm{a, b, c}{/tex} and {tex}\mathrm d{/tex} are measured with percentage error {tex} 1 \% , 2 \% , 3 \% {/tex} and {tex} 4 \% {/tex} respectively. Quantity {tex}\mathrm P {/tex} is calculated as follows<br>{tex} \mathrm { P } = \frac { a ^ { 3 } b ^ { 2 } } { c d } \% {/tex} error in {tex} \mathrm { P } {/tex} is<br>
Question 69 :
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 70 :
The refractive index of water measured by the relation {tex} \mu = \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 71 :
Surface tension of a liquid is 70 dyne/cm. Its value in SI is
Question 72 :
The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula {tex} \mathrm { P } = \frac { \mathrm { F } } { \ell ^ { 2 } } {/tex}. If the maximum errors in the measurement of force and length are {tex} 6 \% {/tex} and {tex} 3 \% {/tex} respectively, then the maximum error in the measurement of pressure is<br>
Question 73 :
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 74 :
Which one of the following is not measured in units of energy?
Question 75 :
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 76 :
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 77 :
Write the dimensions of a {tex} \times b {/tex} in the relation {tex} E = \frac { b - x ^ { 2 } } { a t } , {/tex} where {tex} E {/tex} is the energy, {tex} x {/tex} is the displacement and {tex} t {/tex} is time
Question 78 :
In a simple pendulum experiment, the maximum percentage error in the measurement of length is {tex} 2 \% {/tex} and that in the observation of the time-period is {tex} 3 \% . {/tex} Then the maximum percentage error in determination of the acceleration due to gravity {tex} \mathrm { g } {/tex} is
Question 79 :
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 80 :
A physical quantity of the dimensions of length that can be formed out of {tex} \mathrm { c } , \mathrm { G } {/tex} and {tex} \frac { { e } ^ { 2 } } { 4 \pi \varepsilon _ { 0 } } {/tex} is [{tex} \mathrm { c }{/tex} is velocity of light, {tex} \mathrm { G }{/tex} is universal constant of gravitation and {tex} { e }{/tex} is charge]
Question 81 :
If {tex} x {/tex} and {tex} R {/tex} stands for distance. Then which of the following is dimensionally same as {tex} \int \frac { \operatorname { Rd } x } { x ^ { 2 } } ? {/tex}
Question 84 :
A physical quantity {tex} P {/tex} is described by the relation {tex} P = a ^ { 1 / 2 } b ^ { 2 } c ^ { 3 } d ^ { - 4 } {/tex}. If the relative errors in the measurement of {tex} a , b , c {/tex} and {tex} d {/tex} respectively, are {tex} 2 \% , 1 \% , 3 \% {/tex} and {tex} 5 \% {/tex}, then the relative error in {tex} P {/tex} will be:
Question 85 :
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
Question 86 :
{tex}\mathrm{Assertion} :{/tex} When we change the unit of measurement of a quantity, its numerical value changes.<br>{tex}\mathrm{Reason} :{/tex} Smaller the unit of measurement smaller is its numerical value.
Question 87 :
The numerical values of young's modulus in S.I. unit is {tex} \beta . {/tex} What is its numerical value in cgs system?
Question 88 :
Consider the following statements and select the correct statement(s).<br>I. Optics deal with the phenomena involving light. <br>II. Unification means physical phenomena in terms of few concepts and laws. <br>III. Macroscopic domain of Physics deals with the constitution and structure of matter at the minute scales of atoms and nuclei.<br>
Question 89 :
A quantity {tex} X {/tex} is given by {tex} \varepsilon _ { 0 } L \frac { \Delta V } { \Delta t } {/tex} where {tex} \epsilon _ { 0 } {/tex} is the permittivity of the free space, {tex} L {/tex} is a length, {tex} \Delta V {/tex} is a potential difference and {tex} \Delta t {/tex} is a time interval. The dimensional formula for {tex} X {/tex} is the same as that of
Question 90 :
The period of a body under SHM is represented by {tex} \mathrm { T } = \mathrm { P^a } \mathrm { D } ^ { \mathrm { b } } \mathrm { S } ^ { \mathrm { c } } ; {/tex} where {tex} \mathrm { P } {/tex} is pressure, {tex} \mathrm { D } {/tex} is density and {tex} \mathrm { S } {/tex} is surface tension. The value of {tex} \mathrm { a , b}{/tex} and {tex}\mathrm{c}{/tex} are.
Question 92 :
With the usual notations, the following equation {tex} S _ { t } = u + \frac { 1 } { 2 } a ( 2 t - 1 ) {/tex} is
Question 93 :
The density of material in CGS system of units is 4{tex} \mathrm { g } / \mathrm { cm } ^ { 3 } . {/tex} In a system of units in which unit of length is 10{tex} \mathrm { cm } {/tex} and unit of mass is 100{tex} \mathrm { g } {/tex} , the value of density of material will be
Question 94 :
Match the following :<br>{tex} \begin{array} { l l } { } { \text { Column } \mathrm { I } } & { \text { Column } \mathrm { II } } \\ { \text { (A) Joule } } & { \text { (1) } \mathrm { MLT } ^ { - 2 } } \\ { \text { (B) Newton } } & { \text { (2) } \mathrm { ML } ^ { - 1 } \mathrm { T } - 2 } \\ { \text { (C) Hertz } } & { \text { (3) } \mathrm { ML } ^ { 2 } \mathrm { T } - 2 } \\ { \text { (D) Pascal } } & { \text { (4) } \mathrm { M } ^ { 0 } \mathrm { L } ^ { 0 } \mathrm { T } ^ { - 1 } } \end{array} {/tex}
Question 95 :
The momentum of an electron in an orbit is {tex} h / \lambda {/tex} where {tex} h {/tex} is a constant and {tex} \lambda {/tex} is wavelength associated with it. The nuclear magneton of electron of charge {tex} e {/tex} and mass {tex} m _ { e } {/tex} is given as {tex} \mu _ { n } {/tex} {tex} = \frac { e h } { 3672 \pi m _ { e } } . {/tex} The dimensions of {tex} \mu _ { n } {/tex} are {tex} ( A \rightarrow \text { current } ) {/tex}<br>
Question 96 :
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 97 :
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 98 :
The electric field is given by {tex} \vec { E } = \frac { A } { x ^ { 3 } } \hat { i } + B 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} x {/tex}, {tex}\mathrm{y}{/tex} and {tex}\mathrm{z}{/tex} are in {tex} \mathrm { m } {/tex} ]
Question 99 :
Which of the following statements is/are correct?<br>I. 345.726 has six significant figures.<br>II. 0.004289 has seven singificant figures.<br> III. 125000 has three significant figures.<br> IV. 9.0042 has five significant figures.<br>
Question 100 :
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 102 :
In the equation {tex} P = \frac { R T } { V - b } e ^ { \frac { a V } { R T } } {/tex} {tex} V = {/tex} volume, {tex} P = V - b {/tex} constant, and {tex} T = {/tex} temperature The dimensional formula of a is same as that of
Question 104 :
When a small sphere moves at low speed through a fluid, the viscous force {tex} F {/tex}, opposing the motion is experimentally found to depend upon the radius {tex} r , {/tex} the velocity {tex} v {/tex} of the sphere and the viscosity {tex} \eta {/tex} of the fluid. Expression for force is
Question 106 :
Match the Column I and Column II.<br> {tex} \begin{array} {| l| l| }\hline{ \text { Column I } } & { \text { Column II } } \\ \hline{ \text { (A) J C Maxwell } } & { \text { (1) Verified experimentally the prediction of electromagnetic force } } \\ \hline { \text { (B) Cario Rubia } } & { \text { (2) Unified electricity, magnetism and optics, showed that light is an EM waves} } \\ \hline { \text { (C) Isaac Newton } }& { \text { (3) Unified celestial and terrestrial mechanics} } \\ \hline{ \text { (D) Michael Faraday } } & { \text { (4) Showed that electric and magnetic phenomenon i.e., electromagnetism } }\\ \hline \end{array} {/tex}
Question 107 :
Which of the following is the correct decreasing order of the strengths of four fundamental forces of nature?
Question 108 :
An atomic clock has an accuracy of {tex} 1 {/tex} part is {tex} 10 ^ { 10 } {/tex}. If two such clocks are operated with precision, then after running for {tex} 2500 {/tex} years these will record a difference of nearly.
Question 109 :
{tex} \begin{array} { l l } { \text { Column I } } & { \text { Column II } } \\ { \text { (A) Length } } & { \text { (1) burette } } \\ { \text { (B) Volume } } & { \text { (2) Vernier callipers } } \\ { \text { (C) Diameter of a thin wire } } & { \text { (3) screw gauge } } \\ { \text { (D) Mass } } & { \text { (4) common balance } } \end{array} {/tex}
Question 110 :
The displacement of a body at a particular second {tex} \mathrm { n } {/tex} is given by the expression {tex} \mathrm { S } _ { \mathrm { nth } } = \mathrm { u } + \frac { \mathrm { a } } { 2 } ( 2 \mathrm { n } - 1 ) . {/tex} The dimensional formula of {tex} \mathrm { S } _ { \mathrm { nth } } {/tex} in this equation is
Question 112 :
Match the Column I and Column II.<br> {tex} \begin{array} { l l }{ \text { Column I } } & { \text { Column II } } \\ { \text { (A) Johannes Kepler } } & { \text { (1) Nuclear model of the atom } } \\ { \text { (B) Tycho Brahe } } & { \text { (2) Planetary motion } } \\ { \text { (C) Nicolas Copernicus } }& { \text { (3 ) Elliptical orbit theory } } \\ { \text { (D) Ernest Rutherford } } & { \text { (4) Circular orbit theory } } \end{array} {/tex}
Question 113 :
Surface tension of a liquid is {tex} 70 \mathrm {\ dyne } / \mathrm { cm } {/tex}. Its value in SI is
Question 115 :
The frequency (f) of a wire oscillating with a length {tex} \ell , {/tex} in {tex} \mathrm { p } {/tex} loops, under a tension {tex} \mathrm T {/tex} is given by {tex} \mathrm { f } = \frac { \mathrm { p } } { 2 \ell } \sqrt { \frac { \mathrm { T } } { \mu } } {/tex} where {tex} \mu = {/tex} linear density of the wire. If the error made in determing length, tension and linear density be {tex} 1 \% , - 2 \% {/tex} and {tex} 4 \% , {/tex}, then find the percentage error in the calculated frequency.
Question 117 :
A physical quantity {tex} Q {/tex} is related to four observables {tex} x , y , z {/tex} and {tex} t {/tex} by the relation {tex} Q = {/tex}{tex} \frac { x ^ { 2 / 5 } z ^ { 3 } } { y \sqrt { t } } . {/tex} The percentage errors of measurement in {tex} x , y , z {/tex} and {tex} t {/tex} are {tex} 2.5 \% , 2 \% , 0.5 \% {/tex} and {tex} 1 \% {/tex} respectively. The percentage error in {tex} Q {/tex} will be<br>
Question 118 :
In order to measure physical quantities in the sub-atomic world, the quantum theory often employs energy [E], angular momentum [J] and velocity [ c] as fundamental dimensions instead of the usual mass, length and time. Then, the dimension of pressure in this theory is
Question 119 :
Diameter of a steel ball is measured using a Vernier callipers which has divisions of {tex} 0.1 \mathrm { cm } {/tex} on its main scale (MS) and {tex} 10 {/tex} divisions of its vernier scale (VS) match {tex} 9 {/tex} divisions on the main scale. Three such measurements for a ball are given below:<br>{tex} \begin{array} { | c | c | c | } \hline \text { S.No. } & { \mathrm { MS } ( \mathrm { cm } ) } & { \text { VS divisions } } \\ \hline 1 & { 0.5 } & { 8 } \\ \hline 2 . & { 0.5 } & { 4 } \\ \hline 3 . & { 0.5 } & { 6 } \\ \hline \end{array} {/tex}<br>If the zero error is {tex} - 0.03 \mathrm { cm } , {/tex} then mean corrected diameter is
Question 120 :
The resistance of a metal is given by {tex} \mathrm { R } = \frac { \mathrm { V } } { \mathrm { I } } {/tex} where {tex} \mathrm { V } {/tex} is potential difference and I is the current. In a circuit the potential difference across resistance is {tex} \mathrm { V } = ( 8 \pm 0.5 ) \mathrm { V } {/tex} and current in resistance, {tex} \mathrm { I } = ( 2 \pm 0.2 ) \mathrm { A } . {/tex} What is the value of resistance with its percentage error?
Question 121 :
{tex} \mathrm { E } , \mathrm { m } , \mathrm { J } {/tex} and {tex}\mathrm G{/tex} denote energy, mass, angular momentum and gravitational constant respectively, then the unit of {tex} \frac { \mathrm { EJ } ^ { 2 } } { \mathrm { m } ^ { 5 } \mathrm { G } ^ { 2 } } {/tex} is
Question 122 :
Intensity observed in an interference pattern is {tex} I = I _ { 0 } \sin ^ { 2 } \theta \cdot \mathrm { At } \theta = 30 ^ { \circ } {/tex} intensity {tex} I = 5 \pm 0.0020 {/tex} {tex} \mathrm { W } / \mathrm { m } ^ { 2 } . {/tex} Find percentage error in angle if {tex} I _ { 0 } = 20 {/tex} {tex} \mathrm { W } / \mathrm { m } ^ { 2 } . {/tex}
Question 123 :
Mass of a body is {tex} 210 \mathrm { gm } {/tex} and its density is {tex} 7.981 \mathrm { g } / \mathrm { cm } ^ { 3 } {/tex} what will be its volume, with regard to significant digits?
Question 124 :
Error in the measurement of radius of a sphere is {tex} 1 \% . {/tex} Then error in the measurement of volume is
Question 125 :
The current voltage relation of a diode is given by {tex} \mathrm { I } = \left( \mathrm { e } ^ { \text {1000V } / T } - 1 \right) \mathrm { mA } , {/tex} where the applied voltage {tex} \mathrm { V } {/tex} is in volts and the temperature {tex} \mathrm T {/tex} is in degree kelvin. If a student makes an error measuring {tex} \pm 0.01 \mathrm { V } {/tex} while measuring the current of {tex} 5 \mathrm { mA } {/tex} at {tex} 300 \mathrm { K } , {/tex} what will be the error in the value of current in {tex} \mathrm { mA } ? {/tex}
