# JEE Main

Explore popular questions from Physical World and Measurement for JEE Main. This collection covers Physical World and Measurement previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Physical World and Measurement

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Q 1. If we change unit of a physical quantity then

A

its dimension changes.

its dimension remain same.

C

it may change or may not change.

D

its magnitude changes.

##### Explanation

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Q 2. The least count of a stop watch is {tex}\frac{1} { 5} {/tex} s. The time of 20 oscillations of a pendulum is measured to be 25 s. The minimum percentage error in the measurement of time will be

A

{tex}0.1 \% {/tex}

{tex}0.8 \% {/tex}

C

{tex}1.8 \% {/tex}

D

{tex} 8\% {/tex}

##### Explanation

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Q 3. Energy due to position of a particle is given by, {tex} U = \frac { \alpha \sqrt { y } } { y + \beta } , {/tex} where {tex} \alpha {/tex} and {tex} \beta {/tex} are constants, {tex} y {/tex} is distance. The dimensions of {tex} ( \alpha \times \beta ) {/tex} are

A

{tex} \left[ M ^ { 0 } L T ^ { 0 } \right] {/tex}

B

{tex} \left[ M ^ { 1 / 2 } L ^ { 3 / 2 } T ^ { - 2 } \right] {/tex}

C

{tex} \left[ M ^ { 0 } L ^ { - 7 / 2 } T ^ { 0 } \right] {/tex}

{tex} \left[ M L ^ { 7 / 2 } T ^ { - 2 } \right] {/tex}

##### Explanation

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Q 4. A wire is of mass {tex} ( 0.3 \pm 0.003 ) {/tex} gm. The radius is {tex} ( 0.5 \pm 0.005 ) \mathrm { mm } {/tex} and length is {tex} ( 6.0 \pm 0.06 ) \mathrm { cm } {/tex} then {tex} \% {/tex} error in density is

A

3

4

C

6

D

- 2

##### Explanation

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Q 5. The equation of state of some gases can be expressed as {tex} \left( P + \frac { a } { V ^ { 2 } } \right) ( V - b ) = R T . {/tex} Here, {tex} P {/tex} is the pressure, {tex} V {/tex} the volume, {tex} T {/tex} the absolute temperature, and {tex} a , b , R {/tex} are constants. The dimensions of {tex} a {/tex} are

{tex} \left[ M L ^ { 5 } T ^ { - 2 } \right] {/tex}

B

{tex} \left[ M L ^ { - 1 } T ^ { - 2 } \right] {/tex}

C

{tex} \left[ M ^ { 0 } L ^ { 3 } T ^ { 0 } \right] {/tex}

D

{tex} \left[ M ^ { 0 } L ^ { 6 } T ^ { 0 } \right] {/tex}

##### Explanation

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Q 6. We have error in the measurement of length, radius, mass and current of a wire are {tex} 2 \% , 3 \% , 2 \% {/tex} and 1{tex} \% {/tex} then error in its density will be

A

11{tex} \% {/tex}

B

{tex} 8\% {/tex}

{tex}10 \% {/tex}

D

{tex}7 \% {/tex}

##### Explanation

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Q 7. A physical quantity {tex} x {/tex} depends on qualities {tex} y {/tex} and {tex} z {/tex} as follows: {tex} x = A y + B {/tex} tan {tex} C z , {/tex} where {tex} A , B {/tex} and {tex} C {/tex} are constants. Which of the following do not have the same dimensions?

A

{tex} x {/tex} and {tex} B {/tex}

B

{tex} c {/tex} and {tex} z ^ { - 1 } {/tex}

C

{tex} y {/tex} and {tex} B / A {/tex}

{tex} x {/tex} and {tex} A {/tex}

##### Explanation

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Q 8. The force {tex} F {/tex} is given in terms of time {tex} t {/tex} and displacement {tex} x {/tex} by the equation {tex} F = A \cos B x + C \sin D t . {/tex} The dimensions of {tex} \frac { D } { B } {/tex} are

A

{tex} M ^ { 0 } L ^ { 0 } T ^ { 0 } {/tex}

B

{tex} M ^ { 0 } L ^ { 0 } T ^ { - 1 } {/tex}

C

{tex} M ^ { 0 } L ^ { - 1 } T ^ { 0 } {/tex}

{tex} M ^ { 0 } L ^ { 1 } T ^ { - 1 } {/tex}

##### Explanation

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Q 9. The diameter of a wire is measured with a screw gauge having 50 divisions on circular scale and by one complete rotation of circular scale, main scale moves {tex} 0.5 \mathrm { mm } . {/tex} If reading of screw gauge is {tex} 0.250 \mathrm { cm } . {/tex} The minimum percentage error in the reading will be

0.4

B

0.8

C

4

D

5

##### Explanation

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Q 10. The length, width and thickness of a block are {tex} ( 100.0 {/tex} {tex} \pm 0.1 ) \mathrm { cm } , ( 10.00 \pm 0.01 ) \mathrm { cm } {/tex} and {tex} ( 1.000 \pm 0.001 ) \mathrm { cm } {/tex} respectively. The maximum possible error in its volume will be

A

{tex} \pm 0.111 \mathrm { cm } ^ { 3 } {/tex}

B

{tex} \pm 0.012 \mathrm { cm } ^ { 3 } {/tex}

C

{tex} + 0.03 \mathrm { cm } ^ { 3 } {/tex}

None of these

##### Explanation

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Q 11. The dimensional formula of magnetic flux is

{tex} \left[ M L ^ { 2 } T ^ { - 2 } A ^ { - 1 } \right] {/tex}

B

{tex} \left[ M L ^ { 0 } T ^ { - 2 } A ^ { - 2 } \right] {/tex}

C

{tex} \left[ M ^ { 0 } L ^ { - 2 } T ^ { - 2 } A ^ { - 2 } \right] {/tex}

D

{tex} \left[ M L ^ { 2 } T ^ { - 1 } A ^ { 3 } \right] {/tex}

##### Explanation

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Q 12. Error in the measurement of radius of sphere is 2{tex} \% {/tex}. Then error in the calculation of volume will be

A

1{tex} \% {/tex}

B

5{tex} \% {/tex}

C

3{tex} \% {/tex}

6{tex} \% {/tex}

##### Explanation

{tex}V=\frac{4}{3}πR^33%{/tex} ∴ ,% error in {tex}V={/tex} % error in {tex}R{/tex} =3(2%)=6%.

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Q 13. The velocity of water waves may depend on their wavelength {tex} \lambda {/tex} , the density of water {tex} \rho {/tex} and the acceleration due to gravity {tex} g {/tex}. The method of dimensions gives the relation between these quantities as

A

{tex} v ^ { 2 } \propto \lambda g ^ { - 1 } \rho ^ { - 1 } {/tex}

{tex} v ^ { 2 } \propto g \lambda {/tex}

C

{tex} v ^ { 2 } \propto \lambda g \rho {/tex}

D

{tex} v ^ { 2 } \propto g ^ { - 1 } \lambda ^ { 2 } {/tex}

##### Explanation

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Q 14. A dust particle oscillates in air with a time period which depends on atmospheric pressure {tex} P {/tex}, density of air {tex} d {/tex} and energy of the particle {tex} E , {/tex} then time period is proportional to

{tex} P ^ { - \frac { 5 } { 6 } } d ^ { \frac { 1 } { 2 } } E ^ { \frac { 1 } { 3 } } {/tex}

B

{tex} P ^ { \frac { 1 } { 2 } } d ^ { 3 } E ^ { - 2 } {/tex}

C

{tex} P ^ { - \frac { 1 } { 3 } } d ^ { \frac { 1 } { 2 } } E ^ { 2 } {/tex}

D

{tex} P ^ { - 2 } d ^ { - \frac { 1 } { 2 } } E ^ { - 3 } {/tex}

##### Explanation

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Q 15. Which of the following group have different dimension?

A

Potential difference, EMF, voltage

B

Pressure, stress, Young's modulus

C

Heat, energy, work-done

Dipole moment, electric-flux, electric field

##### Explanation

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Q 16. If a copper wire is stretched to make its radius decrease by 0.1{tex} \% {/tex}, then the percentage increase in resistance is approximately

A

0.1{tex} \% {/tex}

B

0.2{tex} \% {/tex}

0.4{tex} \% {/tex}

D

0.8{tex} \% {/tex}

##### Explanation

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Q 17. Two resistances of 400 {tex}\Omega{/tex} and 800 {tex}\Omega{/tex} connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance 10,000 {tex}\Omega{/tex} is used to measure the potential difference across 400 {tex}\Omega{/tex}. The error in the measurement of potential difference in volts approximately is

A

0.01

B

0.02

0.04

D

0.05

##### Explanation

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Q 18. If there is a positive error of 50{tex} \% {/tex} in the measurement of velocity of a body, then the error in the measurement of kinetic energy is

A

25{tex} \% {/tex}

B

50{tex} \% {/tex}

C

100{tex} \% {/tex}

125{tex} \% {/tex}

##### Explanation

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Q 19. The pitch of a screw gauge is 1{tex} \mathrm { mm } {/tex} and there are 100 divisions on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies 4 divisions below the reference line. When a steel wire is placed between the jaws, two main scale divisions are clearly visible and 67 divisions on the circular scale are observed. The diameter of the wire is

A

2.71{tex} \mathrm { mm } {/tex}

B

2.67{tex} \mathrm { mm } {/tex}

2.63{tex} \mathrm { mm } {/tex}

D

2.65{tex} \mathrm { mm } {/tex}

##### Explanation

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Q 20. Charge on the capacitor is given by {tex}Q=I\alpha e^{- \frac{tI}{{\triangle V}\epsilon_0\beta}}{/tex} where {tex}\alpha{/tex} and {tex}\beta{/tex} are constant, t = time, I = current, {tex} \triangle V{/tex} = Potential difference then, dimension of {tex} \frac{\beta}{\alpha}{/tex} is same as dimension of

{tex}\frac{1}{\sqrt{\mu_0 \epsilon_0}}{/tex}

B

{tex} \mu _ { 0 } \varepsilon _ { 0 } {/tex}

C

{tex} \frac { \mu _ { 0 } } { \varepsilon _ { 0 } } {/tex}

D

{tex} \frac { 1 } { \mu _ { 0 } \varepsilon _ { 0 } } {/tex}

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Q 21. If the speed of light {tex} ( c ) , {/tex} acceleration due to gravity {tex} ( g ) {/tex} and pressure {tex} ( p ) {/tex} are taken as fundamental units, the dimensional formula of gravitational constant {tex} ( G ) {/tex} will be

A

{tex} c ^ { 0 } g p ^ { - 3 } {/tex}

B

{tex} c ^ { 2 } g ^ { 3 } p ^ { - 2 } {/tex}

{tex} c ^ { 0 } g ^ { 2 } p ^ { - 1 } {/tex}

D

{tex} c ^ { 2 } g ^ { 2 } p ^ { - 2 } {/tex}

##### Explanation

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Q 22. Energy due to position of a particle is given by, {tex} U = \frac { \alpha \sqrt { y } } { y + \beta } , {/tex} where {tex} \alpha {/tex} and {tex} \beta {/tex} are constants, {tex} y {/tex} is distance. The dimensions of {tex} ( \alpha \times \beta ) {/tex} are

A

{tex} \left[ M ^ { 0 } L T ^ { 0 } \right] {/tex}

B

{tex} \left[ M ^ { 1 / 2 } L ^ { 3 / 2 } T ^ { - 2 } \right] {/tex}

C

{tex} \left[ M ^ { 0 } L ^ { - 7 / 2 } T ^ { 0 } \right] {/tex}

{tex} \left[ M L ^ {5 / 2 } T ^ { - 2 } \right] {/tex}

##### Explanation

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Q 23. Which of the following is not branch of physics?

A

Mechancis

B

Optics

Cytogenetics

D

Electrodynamics

##### Explanation

Among the given branches, cytogenetics is the branch of biology.

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Q 24. Which of the following statement is correct?

Newton belonged to U.K., who discovered law of gravitation

B

Einstein belonged to England, who discovered laws of photoelectric effect

C

John Bardeen belonged to France, who discovered transistors

D

W.K. Roentgen belonged to Holland, who discovered X-rays

##### Explanation

Name|Discovery|Country of Origin|
Isaac Newton|Universal law of gravitation, Laws of motion, Reflecting telescope|U.K.|
Albert Einstein|Laws of photoelectric effect, Theory of relativity|Germany |
John Bardeen|Transistors, Theory of Superconductivity|U.S.A|
W.K. Roentgen|X - rays|Germany|

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Q 25. Sir C.V. Raman got Nobel Prize in physics for

A

Refraction of light

B

Reflection of light

Scattering of light

D

Dispersion of light

##### Explanation

Sir C.V. Raman got Noble prize for Raman effect, Which deals with scattering of light.