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JEE Advanced > Physical World and Measurement

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

Q 1.

Correct4

Incorrect-1

The dimension of {tex} \left(\frac { 1 } { 2 } \right) \varepsilon _ { 0 } E ^ { 2 }{/tex}({tex} \varepsilon _ { 0 }: {/tex} permittivity of free space, {tex} E{/tex} electric field)

A

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

B

{tex} M L ^ { 2 } T ^ { - 2 } {/tex}

{tex} M L ^ { - 1 } T ^ { - 2 } {/tex}

D

{tex} M L ^ { 2 } T ^ { - 1 } {/tex}

Explanation

Q 2.

Correct4

Incorrect-1

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

A

resistance

B

charge

C

voltage

current

Explanation

Q 3.

Correct4

Incorrect-1

A cube has a side of length {tex} 1.2 \times 10 ^ { - 2 } \mathrm { m } {/tex}. Calculate its volume.

{tex} 1.7 \times 10 ^ { - 6 } \mathrm { m } ^ { 3 } {/tex}

B

{tex} 1.73 \times 10 ^ { - 6 } \mathrm { m } ^ { 3 } {/tex}

C

{tex} 1.70 \times 10 ^ { - 6 } \mathrm { m } ^ { 3 } {/tex}

D

{tex} 1.732 \times 10 ^ { - 6 } \mathrm { m } ^ { 3 } {/tex}

Explanation

Q 4.

Correct4

Incorrect-1

Pressure depends on distance as, {tex} P = \frac { \alpha } { \beta } \exp \left( - \frac { \alpha z } { k \theta } \right) {/tex}, where {tex} \alpha , \beta {/tex} are constants, {tex} z {/tex} is distance, {tex} k {/tex} is Boltzman's constant and {tex} \theta {/tex} is temperature. The dimension of {tex} \beta {/tex} are

A

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

B

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

{tex} M ^ { 0 } L ^ { 2 } T ^ { 0 } {/tex}

D

{tex} M ^ { - 1 } L ^ { 1 } T ^ { 2 } {/tex}

Explanation

Q 5.

Correct4

Incorrect-1

A wire of length {tex} \ell = 6 \pm 0.06 \mathrm { cm } {/tex} and radius {tex} r = 0.5 \pm 0.005 \mathrm { cm } {/tex} and mass {tex} m = 0.3 \pm 0.003 \mathrm { gm } . {/tex} Maximum percentage error in density is

4

B

2

C

1

D

6.8

Explanation

Q 6.

Correct4

Incorrect-1

Which of the following set have different dimensions?

A

Pressure, Young's modulus, Stress

B

EMF, Potential difference, Electric potential

C

Heat, Work done, Energy

Dipole moment, Electric flux, Electric field

Explanation

Q 7.

Correct4

Incorrect-1

In a screw gauge, the zero of mainscale coincides with fifth division of circular scale in figure (i). The circular division of screw gauge are {tex} 50 . {/tex} It moves {tex} 0.5 \mathrm { mm } {/tex} on main scale in one rotation. The diameter of the ball in figure (ii) is

A

{tex} 2.25 \mathrm { mm } {/tex}

B

{tex} 2.20 \mathrm { mm } {/tex}

{tex} 1.20 \mathrm { mm } {/tex}

D

{tex} 1.25 \mathrm { mm } {/tex}

Explanation

Q 8.

Correct4

Incorrect-1

A student performs an experiment for determination of {tex} g \left( = \frac { 4 \pi ^ { 2 } \ell } { T ^ { 2 } } \right) . {/tex} The error in length {tex} \ell {/tex} is {tex} \Delta \ell {/tex} and in time {tex} T {/tex} is {tex} \Delta T {/tex} and {tex} n {/tex} is number of times the reading is taken. The measurement of {tex} g {/tex} is most accurate for

A

{tex}\mathrm {\Delta \ell - 5\ mm; \ \Delta T - 0.2\ sec;\ }n - 10{/tex}

B

{tex}\mathrm {\Delta \ell - 5\ mm; \ \Delta T - 0.2\ sec;\ }n - 20{/tex}

C

{tex}\mathrm {\Delta \ell - 5\ mm; \ \Delta T - 0.1\ sec;\ }n - 10{/tex}

{tex}\mathrm {\Delta \ell - 1\ mm; \ \Delta T - 0.1\ sec;\ }n - 50{/tex}

Explanation

Q 9.

Correct4

Incorrect-1

A student performs an experiment to determine the Young's modulus of a wire, exactly {tex} 2 \mathrm { m } {/tex} long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be {tex} 0.8 \mathrm { mm } {/tex} with an uncertainty of {tex} \pm 0.05 \mathrm { mm } {/tex} at a load of exactly {tex} 1.0 \mathrm { kg } . {/tex} The student also measures the diameter of the wire to be {tex} 0.4 \mathrm { mm } {/tex} with an uncertainty of {tex} \pm 0.01 \mathrm { mm } {/tex}. Take {tex} g = 9.8 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} (exact). The Young's modulus obtained from the reading is

A

{tex} ( 2.0 \pm 0.3 ) \times 10 ^ { 11 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

{tex} ( 2.0 \pm 0.2 ) \times 10 ^ { 11 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

C

{tex} ( 2.0 \pm 0.1 ) \times 10 ^ { 11 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

D

{tex} ( 2.0 \pm 0.05 ) \times 10 ^ { 11 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

Explanation


Q 10.

Correct4

Incorrect-1

Students {tex}I, II{/tex} and {tex}III{/tex} perform an experiment for measuring the acceleration due to gravity ({tex} g {/tex}) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table.
Least count for length {tex} = 0.1 \mathrm { cm } {/tex}
Least count for time {tex} = 0.1 \mathrm { s } {/tex}

If {tex} E _ { I } , E _ { I I } {/tex} and {tex} E _ { III } {/tex} are the percentage errors in {tex} g , {/tex} i.e., {tex} \left( \frac { \Delta g } { g } \times 100 \right) {/tex} for students {tex}I, II{/tex} and {tex}III{/tex}, respectively, then

A

{tex} E _ { I } = 0 {/tex}

{tex} E _ { I } {/tex} is minimum

C

{tex} E _ { I } = E _ { II } {/tex}

D

{tex} E _ { II } {/tex} is maximum

Explanation

Q 11.

Correct4

Incorrect-1

A vernier calipers has {tex} 1 \mathrm { mm } {/tex} marks on the main scale. It has {tex} 20{/tex} equal divisions on the Vernier scale which match with {tex} 16{/tex} main scale divisions. For this Vernier calipers, the least count is

A

{tex} 0.02 \mathrm { mm } {/tex}

B

{tex} 0.05 \mathrm { mm } {/tex}

C

{tex} 0.1 \mathrm { mm } {/tex}

{tex} 0.2 \mathrm { mm } {/tex}

Explanation

Q 12.

Correct4

Incorrect-1

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is {tex} 0.5 \mathrm { mm } {/tex} and there are {tex} 50{/tex} divisions on the circular scale. The reading on the main scale is {tex} 2.5 \mathrm { mm } {/tex} and that on the circular scale is {tex} 20{/tex} divisions. If the measured mass of the ball has a relative error of {tex} 2 \% {/tex}, the relative percentage error in the density is

A

{tex} 0.9 \% {/tex}

B

{tex} 2.4 \% {/tex}

{tex} 3.1 \% {/tex}

D

{tex} 4.2 \% {/tex}

Explanation

Q 13.

Correct4

Incorrect-1

In the determination of Young's modulus {tex}\left(Y = \frac{4MLg}{\pi l d^2}\right){/tex} by using Searle's method, a wire of length {tex}L{/tex} = 2 m and diameter {tex}d{/tex} = 0.5 mm is used. For a load {tex}M{/tex} = 2.5 kg, an extension {tex}l{/tex} = 0.25 mm in the length of the wire is observed. Quantities {tex}d{/tex} and {tex}l{/tex} are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the {tex}Y{/tex} measurement

due to the errors in the measurements of {tex} d {/tex} and {tex} l {/tex} are the same

B

due to the error in the measurement of {tex} d {/tex} is twice that due to the error in the measurement of {tex} l {/tex}

C

due to the error in the measurement of {tex} l {/tex} is twice that due to the error in the measurement of {tex} d {/tex}

D

due to the error in the measurement of {tex} d {/tex} is four times that due to the error in the measurement of {tex} l {/tex}

Explanation

Q 14.

Correct4

Incorrect-1

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm . The 24{tex}^ { \text {th } } {/tex} division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

A

5.112 cm

5.124 cm

C

5.136 cm

D

5.148 cm

Explanation

Q 15.

Correct4

Incorrect-1

There are two Vernier calipers both of which have {tex} 1\ \mathrm { cm } {/tex} divided into {tex}10{/tex} equal divisions on the main scale. The Vernier scale of one of the calipers {tex} \left( \mathrm { C } _ { 1 } \right) {/tex} has {tex}10{/tex} equal divisions that correspond to {tex}9{/tex} main scale divisions. The Vernier scale of the other caliper {tex} \left( \mathrm { C } _ { 2 } \right) {/tex} has {tex}10{/tex} equal divisions that correspond to {tex}11{/tex} main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in {tex} \mathrm { cm } {/tex} ) by calipers {tex} \mathrm { C } _ { 1 } {/tex} and {tex} \mathrm { C } _ { 2 } {/tex}, respectively, are

A

{tex}2.85{/tex} and {tex}2.82{/tex}

{tex}2.87{/tex} and {tex}2.83{/tex}

C

{tex}2.87{/tex} and {tex}2.86{/tex}

D

{tex}2.87{/tex} and {tex}2.87{/tex}

Explanation

Q 16.

Correct4

Incorrect-1

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is {tex} \delta \mathrm T{/tex} = 0.01 seconds and he measures the depth of the well to be {tex} \mathrm { L }{/tex} = 20 meters. Take the acceleration due to gravity {tex} \mathrm { g }{/tex} = 10 ms{tex}^ { - 2 }{/tex} and the velocity of sound is 300 ms{tex}^ { - 1 }{/tex}. Then the fractional error in the measurement, {tex} \delta \mathrm { L } / \mathrm { L }{/tex} , is closest to

A

0.2{tex} \% {/tex}

1{tex} \% {/tex}

C

3{tex} \% {/tex}

D

5{tex} \% {/tex}

Explanation

Q 17.

Correct4

Incorrect-1

Using the expression {tex} 2 \mathrm { d } \sin \theta = \lambda , {/tex} one calculates the values of {tex} \mathrm { d }{/tex} by measuring the corresponding angles {tex} \theta {/tex} in the range 0 to 90{tex} ^ { \circ } . {/tex} The wavelength {tex} \lambda {/tex} is exactly known and the error in {tex} \theta {/tex} is constant for all values of {tex} \theta . {/tex} As {tex} \theta {/tex} increases from {tex} 0 ^ { \circ } {/tex}

A

The absolute error in {tex} d {/tex} remains constant

B

The absolute error in {tex} d {/tex} increases

C

The fractional error in {tex} d {/tex} remains constant

The fractional error in {tex} d {/tex} decreases

Explanation