Explore popular questions from Properties of Bulk Matter for JEE Advanced. This collection covers Properties of Bulk Matter previous year JEE Advanced questions hand picked by experienced teachers.

## Mathematics

Properties of Bulk Matter

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Q 1. Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles traingle {tex} A B C , {/tex} right-angled at {tex} B {/tex}. The points {tex} A {/tex} and {tex} B {/tex} are maintained at temperatures {tex} T {/tex} and {tex} ( \sqrt { 2 } ) T {/tex} respectively. In the steady state, the temperature of the point {tex} C {/tex} is {tex} T _ { c } {/tex}. Assuming that only heat conduction takes place, {tex} T _ { c } / T {/tex} is

A

{tex} \frac { 1 } { 2 ( \sqrt { 2 } - 1 ) } {/tex}

{tex} \frac { 3 } { \sqrt { 2 } + 1 } {/tex}

C

{tex} \frac { 1 } { \sqrt { 3 } ( \sqrt { 2 } - 1 ) } {/tex}

D

{tex} \frac { 1 } { \sqrt { 2 } + 1 } {/tex}

##### Explanation

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Q 2. Which of the following graphs correctly represents the variation of {tex} \beta = - \frac { d V / d P } { V } {/tex} with {tex} P {/tex} for an ideal gas at constant temperature?

B

C

D

##### Explanation

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Q 3. An ideal Black-body at room temperature is thrown into a furnace. It is observed that

initially it is the darkest body and at later times the brightest

B

it is the darkest body at all times

C

it cannot be distinguished at all times

D

initially it is the darkest body and at later times it cannot be distinguished

##### Explanation

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Q 4. The graph, shown in the adjacent diagram, represents the variation of temperature (T) of two bodies, {tex} x {/tex} and {tex} y {/tex} having same surface area, with time {tex} ( t ) {/tex} due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies

A

{tex} E _ { x } > E _ { y }\ \& \ a _ { x } < a _ { y } {/tex}

B

{tex} E _ { x } < E _ { y }\ \& \ a _ { x } > a _ { y } {/tex}

{tex} E _ { x } > E _ { y }\ \& \ a _ { x } > a _ { y } {/tex}

D

{tex} E _ { x } < E _ { y }\ \& \ a _ { x } < a _ { y } {/tex}

##### Explanation

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Q 5. Two moles of ideal helium gas are in a rubber balloon at {tex} 30 ^ { \circ } \mathrm { C } {/tex}. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to {tex} 35 ^ { \circ } \mathrm { C } {/tex}. The amount of heat required in raising the temperature is nearly (take {tex} R {/tex} {tex} = 8.31 \mathrm { J } / \mathrm { mol . K } {/tex} )

A

{tex} 62 \mathrm { J } {/tex}

B

{tex} 104 \mathrm { J } {/tex}

C

{tex} 124 \mathrm { J } {/tex}

{tex} 208 \mathrm { J } {/tex}

##### Explanation

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Q 6. A hemispherical portion of radius {tex} R {/tex} is removed from the bottom of a cylinder of radius {tex} R {/tex}. The volume of the remaining cylinder is {tex} V {/tex} and its mass {tex} M . {/tex} It is suspended by a string in a liquid of density {tex} \rho {/tex} where it stays vertical. The upper surface of the cylinder is at a depth {tex} h {/tex} below the liquid surface. The force on the bottom of the cylinder by the liquid is

A

{tex} M g {/tex}

B

{tex} M g - V \rho g {/tex}

C

{tex} M g + \pi R ^ { 2 } h \rho g {/tex}

{tex} \rho g \left( V + \pi R ^ { 2 } h \right) {/tex}

##### Explanation

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Q 7. A glass tube of uniform internal radius ( {tex} \mathrm { r } {/tex} ) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position.{tex}\mathrm{End}\ 1{/tex} has a hemispherical soap bubble of radius {tex} \mathrm { r } {/tex}. {tex}\mathrm{End}\ 2{/tex} has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

A

air from end 1 flows towards end 2. No change in the volume of the soap bubbles

air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases

C

no changes occurs

D

air from end 2 flows towards end 1. volume of the soap bubble at end 1 increases

##### Explanation

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Q 8. A marble of mass {tex} x {/tex} and diameter {tex} 2 r {/tex} is gently released in a tall cylinder containing honey. If the marble displaces mass {tex} y ( < x ) {/tex} of the liquid, then the terminal velocity is proportional to

A

{tex} x + y {/tex}

B

{tex} x - y {/tex}

C

{tex} \frac { x + y } { r } {/tex}

{tex} \frac { x - y } { r } {/tex}

##### Explanation

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Q 9. Two rods of different materials having coefficients of linear expansion {tex} \alpha _ { 1 } {/tex} and {tex} \alpha _ { 2 } {/tex} and Young's moduli, {tex} Y _ { 1 } {/tex} and {tex} Y _ { 2 } , {/tex} respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If {tex} \alpha _ { 1 } / \alpha _ { 2 } = 2 / 3 , {/tex} then the thermal stresses developed in the two rods are equal, provided {tex} Y _ { 1 } / Y _ { 2 } {/tex} is equal to

A

2:3

B

1:1

3:2

D

4:9

##### Explanation

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Q 10. A small but heavy block of mass {tex} 10 \mathrm { kg } {/tex} is attached to a wire {tex} 0.3 \mathrm { m } {/tex} long. Its breaking stress is {tex} 4.8 \times {/tex} {tex} 10 ^ { 7 } \mathrm { N } / \mathrm { m } ^ { 2 } . {/tex} The area of the cross section of the wire is {tex} 10 ^ { - 6 } \mathrm { m } ^ { 2 } . {/tex} The maximum angular velocity with which the block can be rotated in the horizontal circle is

{tex} 4 \mathrm { rad } / \mathrm { s } {/tex}

B

{tex} 8 \mathrm { rad } / \mathrm { s } {/tex}

C

{tex} 10 \mathrm { rad } / \mathrm { s } {/tex}

D

{tex} 32 \mathrm { rad } / \mathrm { s } {/tex}

##### Explanation

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Q 11. A solid sphere of radius {tex} R , {/tex} made up of a material of bulk modulus {tex} K {/tex} is surrounded by a liquid in a cylindrical container. A massless piston of area {tex} A {/tex} floats on the surface of the liquid. When a mass {tex} M {/tex} is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is

A

{tex} \frac { M g } { A K } {/tex}

{tex} \frac { M g } { 3 A K } {/tex}

C

{tex} \frac { 3 M g } { A K } {/tex}

D

{tex} \frac { M g } { 2 A K } {/tex}

##### Explanation

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Q 12. A material has normal density {tex} \rho {/tex} and bulk modulus {tex} K . {/tex} The increase in the density of the material when it is subjected to an external pressure {tex} P {/tex} from all sides is

A

{tex} P / \rho K {/tex}

B

{tex} K / \rho P {/tex}

{tex} \rho P / K {/tex}

D

{tex} \rho K / P {/tex}

##### Explanation

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Q 13. Eight identical spherical rain drops are falling down with terminal velocity {tex} v {/tex}. If they combine to form one big spherical drop, its terminal velocity will be

A

{tex} \frac { v } { 2 } {/tex}

B

{tex} 2 v {/tex}

{tex} 4 v {/tex}

D

{tex} 8 v {/tex}

##### Explanation

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Q 14. In a laminar flow of a liquid through a horizontal capillary tube of radius {tex} r , {/tex} the rate of flow is {tex} Q {/tex} when a pressure difference {tex} P {/tex} is maintained between its ends. The rate of flow through another tube of the same length but radius {tex} r / 2 {/tex} when the pressure difference between its ends is {tex} 2 P {/tex} will be

A

{tex} 8 Q {/tex}

B

{tex} 4 Q {/tex}

C

{tex} \frac { Q } { 4 } {/tex}

{tex} \frac { Q } { 8 } {/tex}

##### Explanation

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Q 15. An electric pump sends a liquid of density {tex} \rho {/tex} through a horizontal pipe of cross-sectional area {tex} a {/tex} with a speed {tex} v {/tex}. The power of the pump is proportional to

A

{tex} v {/tex}

B

{tex} v ^ { 2 } {/tex}

{tex} v ^ { 3 } {/tex}

D

{tex} v ^ { 4 } {/tex}

##### Explanation

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Q 16. A cubical vessel of height {tex} 1 \mathrm { m } {/tex} is full of water. The work done in pumping water out of the vessel is

A

{tex} 49 \mathrm { J } {/tex}

B

{tex} 98 \mathrm { J } {/tex}

{tex} 4900 \mathrm { J } {/tex}

D

{tex} 9800 \mathrm { J } {/tex}

##### Explanation

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Q 17. Two spheres of equal masses but radii {tex} R {/tex} and {tex} 2 R {/tex} are allowed to fall in a liquid. The ratio of their terminal velocities is

A

{tex}1:4{/tex}

B

{tex}1:2{/tex}

C

{tex}1:32{/tex}

{tex}2:1{/tex}

##### Explanation

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Q 18. A volume {tex} V {/tex} of a viscous liquid flows per second due to a pressure head {tex} \Delta P {/tex} along a pipe of diameter {tex} d {/tex} and length {tex} l {/tex}. Instead of this pipe, a set of four pipes each of diameter {tex} d / 2 {/tex} and length {tex} 2 l {/tex} is connected to the same pressure head {tex} \Delta P {/tex}. The volume of the liquid flowing per second now is

A

{tex} V {/tex}

B

{tex} \frac { V } { 4 } {/tex}

{tex} \frac { V } { 8 } {/tex}

D

{tex} \frac { V } { 16 } {/tex}

##### Explanation

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Q 19. Water from a tap emerges vertically downwards with an initial speed of {tex} 1.0 \mathrm { ms } ^ { - 1 } . {/tex} The cross-sectional area of the tap is {tex} 10 ^ { - 4 } \mathrm { m } ^ { 2 } . {/tex} Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream {tex} 0.15 \mathrm { m } {/tex} below the tap is (take {tex} g = 10 \mathrm { ms } ^ { - 2 } {/tex} )

A

{tex} 5.0 \times 10 ^ { - 4 } \mathrm { m } ^ { 2 } {/tex}

B

{tex} 1.0 \times 10 ^ { - 5 } \mathrm { m } ^ { 2 } {/tex}

{tex} 5.0 \times 10 ^ { - 5 } \mathrm { m } ^ { 2 } {/tex}

D

{tex} 2.0 \times 10 ^ { - 5 } \mathrm { m } ^ { 2 } {/tex}

##### Explanation

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Q 20. Water stands at a depth {tex} H {/tex} in a tank whose side walls are vertical. A hole is made in one of the walls at a height {tex} h {/tex} below the water surface. The stream of water emerging from the hole strikes the floor at a distance {tex} R {/tex} from the tank, where {tex} R {/tex} is given by

A

{tex} R = \sqrt { h ( H - h ) } {/tex}

B

{tex} R = \sqrt { h ( H + h ) } {/tex}

{tex} R = 2 \sqrt { h ( H - h ) } {/tex}

D

{tex} R = 2 \sqrt { h ( H + h ) } {/tex}

##### Explanation

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Q 21. A cylindrical tank having cross-sectional area {tex} A {/tex} is filled with water to a height of {tex} 2.0 \mathrm { m } {/tex}. A circular hole of cross-sectional area {tex} a {/tex} is opened at a height of {tex} 75 \mathrm { cm } {/tex} from the bottom. If {tex} \frac { a } { A } = \sqrt { 0.2 } {/tex}, the velocity with which water emerges from the hole is {tex} \left( g = 9.8 \mathrm { ms } ^ { - 2 } \right) . {/tex}

A

{tex} 4.9 \mathrm { ms } ^ { - 1 } {/tex}

B

{tex} 4.95 \mathrm { ms } ^ { - 1 } {/tex}

{tex} 5.0 \mathrm { ms } ^ { - 1 } {/tex}

D

{tex} 5.5 \mathrm { ms } ^ { - 1 } {/tex}

##### Explanation

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Q 22. A small metal sphere of radius {tex} r {/tex} and density {tex} \rho {/tex} falls from rest in a viscous liquid of density {tex} \sigma {/tex} and coefficient of viscosity {tex}\eta{/tex}. Due to friction heat is produced. The rate of production of heat when the sphere has acquired the terminal velocity is proportional to

A

{tex} r ^ { 2 } {/tex}

B

{tex} r ^ { 3 } {/tex}

C

{tex} r ^ { 4 } {/tex}

{tex} r ^ { 5 } {/tex}