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States of Matter: Gases and Liquids
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s-Block Element (Alkali and Alkaline earth metals)
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Gravitation

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Q 1. The Fig. shows a planet in elliptical orbit around the sun {tex} S {/tex}. Where is the kinetic energy of the planet maximum?

{tex} P_1 {/tex}

{tex} P _ { 2 } {/tex}

{tex} P _ { 3 } {/tex}

{tex} P_4 {/tex}

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Q 2. The ratio of the radii of the planets {tex} P _ { 1 } {/tex} and {tex} P _ { 2 } {/tex} is {tex} k _ { 1 } {/tex} . The ratio of the acceleration due to the gravity on them is {tex} k _ { 2 } . {/tex} The ratio of the escape velocities from them will be

{tex} k _ { 1 } k _ { 2 } {/tex}

{tex} \sqrt { k _ { 1 } k _ { 2 } } {/tex}

{tex} \sqrt { \left( k _ { 1 } / k _ { 2 } \right) } {/tex}

{tex} \sqrt { \left( k _ { 2 } / k _ { 1 } \right) } {/tex}

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Q 3. Which of the following graphs represent correctly the variation of intensity of gravitational field {tex} l {/tex} with the distance {tex} r {/tex} from the centre of a spherical shell of mass {tex} M {/tex} and radius {tex} a ? {/tex}

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Q 4. The period of a satellite in a circular orbit of radius {tex} R {/tex} is {tex} T {/tex} . The period of another satellite in a circular orbit of radius {tex}4R {/tex} is

{tex}4\ T {/tex}

{tex} T / 4 {/tex}

{tex}8\ T {/tex}

{tex} T / 8 {/tex}

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Q 5. An artificial satellite moving in a circular orbit around the earth has a total energy{tex} (KE + \mathrm { PE } ){/tex} is {tex} E _ { 0 } {/tex}. Its potential energy is

{tex} - E _ { 0 } {/tex}

{tex}1.5E _ { 0 } {/tex}

{tex}2 E _ { 0 } {/tex}

{tex} E _ { 0 } {/tex}

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Q 6. A simple pendulum has a time period {tex}T_1{/tex} when on the earth's surface, and {tex}T_2{/tex} when taken to a height R above the earth's surface, where R is radius of earth. The value of {tex}T_2/T_1{/tex} is

{tex}1{/tex}

{tex} \sqrt { 2 } {/tex}

{tex}4{/tex}

{tex}2{/tex}

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Q 7. A body of mass {tex} m {/tex} rises to a height {tex} h = R / 5 {/tex} from the earth's surface where {tex} R {/tex} is radius of the earth. If {tex} g {/tex} is acceleration due to gravity at the earth surface, the increase in potential energy is

{tex} m g R {/tex}

{tex} ( 4 / 5 ) m g R {/tex}

{tex} ( 1 / 6 ) m g R {/tex}

{tex} ( 6 / 7 ) m g R {/tex}

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Q 8. Imagine a light planet revolving around a very massive star in a circular orbit of radius {tex} R {/tex} with a period of revolution {tex} T . {/tex} If the gravitational force of attraction between the planet and the star is proportional to {tex} R ^ { - 5 / 2 } {/tex} , {tex} T ^ { 2 } {/tex} is proportional to

{tex} R ^ { 3 } {/tex}

{tex} R ^ { 7 / 2 } {/tex}

{tex} R ^ { 3 / 2 } {/tex}

{tex} R ^ { 3.75 } {/tex}

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Q 9. The orbital velocity of an artificial satellite in a circular orbit just above earth's surface is {tex} v _ { 0 } {/tex} . For a satellite orbiting in a circular orbit at an altitude of half of earth's radius is

{tex} \sqrt { \frac { 3 } { 2 } } v _ { 0 } {/tex}

{tex} \sqrt { \frac { 2 } { 3 } } v _ { 0 } {/tex}

{tex} \frac { 3 } { 2 } v _ { 0 } {/tex}

{tex} \frac { 2 } { 3 } v _ { 0 } {/tex}

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Q 10. A particle is placed in a field characterized by a value of gravitational potential given by {tex} V = - k x y , {/tex} where {tex} k {/tex} is a constant. If {tex} \vec { E } _ { g } {/tex} is the gravitational field then,

{tex} \vec { E } _ { g } = k ( x \hat { i } + y \hat { j } ) {/tex} and is conservative in nature.

{tex} \vec { E } _ { g } = k ( y \hat { i } + x \hat { j } ) {/tex} and is conservative in nature.

{tex} \vec { E } _ { g } = k ( x \hat { i } + y \hat { j } ) {/tex} and is non-conservative in nature

{tex} \vec { E } _ { g } = k ( y \hat { i } + x \hat { j } ) {/tex} and is non-conservative in nature.

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Q 11. If three uniform spheres, each having mass {tex} M {/tex} and radius {tex} R , {/tex} are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

{tex} \frac { G M ^ { 2 } } { 4 R ^ { 2 } } {/tex}

{tex} \frac { 2 G M ^ { 2 } } { R ^ { 2 } } {/tex}

{tex} \frac { 2 G M ^ { 2 } } { 4 R ^ { 2 } } {/tex}

{tex} \frac { \sqrt { 3 } G M ^ { 2 } } { 4 R ^ { 2 } } {/tex}

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Q 12. The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity.

Will be directed towards the centre but not the same everywhere.

Will have the same value everywhere but not directed towards the centre.

Will be same everywhere in magnitude directed towards the centre.

Cannot be zero at any point.

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Q 13. Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the CM (centre of mass) causing translation and a net torque at the CM causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere).

The torque is zero.

The torque cause the earth to spin.

The rigid body result is not applicable since the earth is not even approximately a rigid body.

The torque causes the earth to move around the sun.

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Q 14. Both the earth and the moon are subject to the gravita- tional force of the sun. As observed from the sun, the orbit of the moon

will be elliptical.

will not be strictly elliptical because the total gravitational force on it is not central.

is not elliptical but will necessarily be a closed curve.

deviates considerably from being elliptical due to influence of planets other than the earth.

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Q 15. Choose the wrong option.

Inertial mass is a measure of difficulty of accel- erating a body by an external force whereas the gravitational mass is relevant in determining the gravitational force on it by an external mass.

That the gravitational mass and inertial mass are equal is an experimental result.

That the acceleration due to gravity on the carth is the same for all bodies is due to the equality of gravitational mass and inertial mass.

Gravitational mass of a particle like proton can depend on the presence of neighbouring heavy objects but the inertial mass cannot.

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Q 16. The kinetic energy needed to project a body of mass {tex} m {/tex} from the earth's surface (radius {tex} R {/tex} ) to infinity is

{tex} \frac { m g R } { 2 } {/tex}

2{tex} m g R {/tex}

{tex} m g R {/tex}

{tex} \frac { m g R } { 4 } {/tex}

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Q 17. Two spherical bodies of mass {tex} M {/tex} and {tex}5 M {/tex} and radii {tex} R {/tex} and {tex}2 R {/tex} respectively, are released in free space with initial separation between their centres equal to {tex}12 R {/tex}. If they attract each other due to gravitational force only, then the distance covered by the smaller body just, before collision is

{tex} 2.5 \ R {/tex}

{tex}4.5\ R {/tex}

{tex}7.5\ R {/tex}

{tex}1.5\ R {/tex}

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Q 18. The escape velocity for a body projected vertically upwards from the surface of earth is {tex}11\ \mathrm { km } \mathrm { s^{-1} } {/tex} . If the body is projected at an angle of {tex} 45 ^ { \circ } {/tex} with the vertical, the escape velocity will be

{tex}11 \sqrt { 2 } \mathrm { km } \mathrm { s^{-1} } {/tex}

{tex}22\ \mathrm { km } \mathrm { s^{-1} } {/tex}

{tex}11\ \mathrm { km } \mathrm { s^{-1} } {/tex}

{tex} \frac { 11 } { \sqrt { 2 } } \mathrm { m } \mathrm { s^{-1} } {/tex}

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Q 19. {tex}Directions :{/tex} The following question contains statement-I and statement-2. Of the four choices given, choose the one that best describes the two statements.

{tex}Statement-1:{/tex} For a mass {tex} M {/tex} kept at the centre of a cube of side {tex} a , {/tex} the flux of gravitational field passing through its sides is {tex} 4 \pi G M . {/tex}

{tex}Statement-2 :{/tex} If the direction of a field due to a point source is radial and its dependence on the a distance {tex} r {/tex} from the source is given as {tex} 1 / r ^ { 2 } , {/tex} its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

Statement-1 is true, statement-2 is false.

Statement-I is false, statement-2 is true.

Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for statement-1.

Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for statement-1.

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Q 20. Two bodies of masses {tex} m {/tex} and 4{tex} m {/tex} are placed at a distance {tex} r . {/tex} The gravitational potential at a point on the line joining them where the gravitational field is zero is:

{tex} - \frac { 4 G m } { r } {/tex}

{tex} - \frac { 6 G m } { r } {/tex}

{tex} - \frac { 9 G m } { r } {/tex}

{tex} \mathrm {zero}{/tex}

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Q 21. If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

continue to move in its orbit with same velocity

move tangentially to the original orbit in the same velocity

become stationary in its orbit

move towards the earth.

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Q 22. The escape velocity of a body depends upon mass as

{tex} m ^ { 0 } {/tex}

{tex} m ^ 1{/tex}

{tex} m ^ { 2 } {/tex}

{tex} m ^ { 3 } {/tex}

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Q 23. The escape velocity for a body projected vertically upwards from the surface of earth is {tex} 11 \mathrm { km } / \mathrm { s } {/tex}. If the body is projected at an angle of {tex} 45 ^ { \circ } {/tex} with the vertical, the escape velocity will be

{tex} 11 \sqrt { 2 } \mathrm { km } / \mathrm { s } {/tex}

{tex} 22 \mathrm { km } / \mathrm { s } {/tex}

{tex} 11 \mathrm { km } / \mathrm { s } {/tex}

{tex} 11 / \sqrt { 2 } \mathrm { m } / \mathrm { s } {/tex}

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Q 24. The time period of an earth satellite in circular orbit is independent of

the mass of the satellite

radius of its orbit

both the mass and radius of the orbit

neither the mass of the satellite nor the radius of its orbit.

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Q 25. Two spherical bodies of mass {tex} M {/tex} and {tex} 5 M {/tex} and radii {tex} R {/tex} and {tex} 2 R {/tex} respectively are released in free space with initial separation between their centres equal to {tex} 12 R {/tex}. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

{tex} 2.5 R {/tex}

{tex} 4.5 R {/tex}

{tex} 7.5 R {/tex}

{tex} 1.5 R {/tex}

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