02. Gravitational Potential Energy, Gravitational Potential
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Gravitation

138478 The mass of the earth is $6.00 \times 10^{24} \mathrm{~kg}$ and that of the moon is $7.40 \times 10^{22} \mathrm{~kg}$. The constant of gravitation $G=6.67 \times 10^{-1 i} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}$. The potential energy of the system is $-7.79 \times 10^{28} \mathrm{~J}$. The mean distance between the earth and moon is

1 $3.80 \times 10^{8} \mathrm{~m}$
2 $3.37 \times 10^{6} \mathrm{~m}$
3 $7.60 \times 10^{4} \mathrm{~m}$
4 $1.90 \times 10^{2} \mathrm{~m}$
JCECE-2008
Gravitation

138479 The gravitational field in a region is given by $\mathrm{g}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathrm{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$. The change in the gravitational potential energy of a particle of mass $1 \mathrm{~kg}$ when it is taken from the origin to a point $(7 m,-3 m)$ is:

1 $71 \mathrm{~J}$
2 $13 \sqrt{58} \mathrm{~J}$
3 $-71 \mathrm{~J}$
4 $1 \mathrm{~J}$
BITSAT-2008
Gravitation

138481 A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be

1 $-\frac{3 \mathrm{GM}}{\mathrm{a}}$
2 $-\frac{2 \mathrm{GM}}{\mathrm{a}}$
3 $-\frac{\mathrm{GM}}{\mathrm{a}}$
4 $-\frac{4 \mathrm{GM}}{\mathrm{a}}$
AIPMT 2010
Gravitation

138482 The potential energy of a satellite of mass $m$ and revolving at a height $R_{e}$ above the surface of earth where $R_{e}$ = radius of earth, is

1 $-m g R_{e}$
2 $\frac{-m g R_{e}}{2}$
3 $\frac{-m g R_{e}}{3}$
4 $\frac{-m g R_{e}}{4}$
BITSAT- 2005
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Gravitation

138478 The mass of the earth is $6.00 \times 10^{24} \mathrm{~kg}$ and that of the moon is $7.40 \times 10^{22} \mathrm{~kg}$. The constant of gravitation $G=6.67 \times 10^{-1 i} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}$. The potential energy of the system is $-7.79 \times 10^{28} \mathrm{~J}$. The mean distance between the earth and moon is

1 $3.80 \times 10^{8} \mathrm{~m}$
2 $3.37 \times 10^{6} \mathrm{~m}$
3 $7.60 \times 10^{4} \mathrm{~m}$
4 $1.90 \times 10^{2} \mathrm{~m}$
JCECE-2008
Gravitation

138479 The gravitational field in a region is given by $\mathrm{g}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathrm{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$. The change in the gravitational potential energy of a particle of mass $1 \mathrm{~kg}$ when it is taken from the origin to a point $(7 m,-3 m)$ is:

1 $71 \mathrm{~J}$
2 $13 \sqrt{58} \mathrm{~J}$
3 $-71 \mathrm{~J}$
4 $1 \mathrm{~J}$
BITSAT-2008
Gravitation

138481 A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be

1 $-\frac{3 \mathrm{GM}}{\mathrm{a}}$
2 $-\frac{2 \mathrm{GM}}{\mathrm{a}}$
3 $-\frac{\mathrm{GM}}{\mathrm{a}}$
4 $-\frac{4 \mathrm{GM}}{\mathrm{a}}$
AIPMT 2010
Gravitation

138482 The potential energy of a satellite of mass $m$ and revolving at a height $R_{e}$ above the surface of earth where $R_{e}$ = radius of earth, is

1 $-m g R_{e}$
2 $\frac{-m g R_{e}}{2}$
3 $\frac{-m g R_{e}}{3}$
4 $\frac{-m g R_{e}}{4}$
BITSAT- 2005
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Gravitation

138478 The mass of the earth is $6.00 \times 10^{24} \mathrm{~kg}$ and that of the moon is $7.40 \times 10^{22} \mathrm{~kg}$. The constant of gravitation $G=6.67 \times 10^{-1 i} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}$. The potential energy of the system is $-7.79 \times 10^{28} \mathrm{~J}$. The mean distance between the earth and moon is

1 $3.80 \times 10^{8} \mathrm{~m}$
2 $3.37 \times 10^{6} \mathrm{~m}$
3 $7.60 \times 10^{4} \mathrm{~m}$
4 $1.90 \times 10^{2} \mathrm{~m}$
JCECE-2008
Gravitation

138479 The gravitational field in a region is given by $\mathrm{g}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathrm{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$. The change in the gravitational potential energy of a particle of mass $1 \mathrm{~kg}$ when it is taken from the origin to a point $(7 m,-3 m)$ is:

1 $71 \mathrm{~J}$
2 $13 \sqrt{58} \mathrm{~J}$
3 $-71 \mathrm{~J}$
4 $1 \mathrm{~J}$
BITSAT-2008
Gravitation

138481 A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be

1 $-\frac{3 \mathrm{GM}}{\mathrm{a}}$
2 $-\frac{2 \mathrm{GM}}{\mathrm{a}}$
3 $-\frac{\mathrm{GM}}{\mathrm{a}}$
4 $-\frac{4 \mathrm{GM}}{\mathrm{a}}$
AIPMT 2010
Gravitation

138482 The potential energy of a satellite of mass $m$ and revolving at a height $R_{e}$ above the surface of earth where $R_{e}$ = radius of earth, is

1 $-m g R_{e}$
2 $\frac{-m g R_{e}}{2}$
3 $\frac{-m g R_{e}}{3}$
4 $\frac{-m g R_{e}}{4}$
BITSAT- 2005
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Gravitation

138478 The mass of the earth is $6.00 \times 10^{24} \mathrm{~kg}$ and that of the moon is $7.40 \times 10^{22} \mathrm{~kg}$. The constant of gravitation $G=6.67 \times 10^{-1 i} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}$. The potential energy of the system is $-7.79 \times 10^{28} \mathrm{~J}$. The mean distance between the earth and moon is

1 $3.80 \times 10^{8} \mathrm{~m}$
2 $3.37 \times 10^{6} \mathrm{~m}$
3 $7.60 \times 10^{4} \mathrm{~m}$
4 $1.90 \times 10^{2} \mathrm{~m}$
JCECE-2008
Gravitation

138479 The gravitational field in a region is given by $\mathrm{g}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathrm{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$. The change in the gravitational potential energy of a particle of mass $1 \mathrm{~kg}$ when it is taken from the origin to a point $(7 m,-3 m)$ is:

1 $71 \mathrm{~J}$
2 $13 \sqrt{58} \mathrm{~J}$
3 $-71 \mathrm{~J}$
4 $1 \mathrm{~J}$
BITSAT-2008
Gravitation

138481 A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be

1 $-\frac{3 \mathrm{GM}}{\mathrm{a}}$
2 $-\frac{2 \mathrm{GM}}{\mathrm{a}}$
3 $-\frac{\mathrm{GM}}{\mathrm{a}}$
4 $-\frac{4 \mathrm{GM}}{\mathrm{a}}$
AIPMT 2010
Gravitation

138482 The potential energy of a satellite of mass $m$ and revolving at a height $R_{e}$ above the surface of earth where $R_{e}$ = radius of earth, is

1 $-m g R_{e}$
2 $\frac{-m g R_{e}}{2}$
3 $\frac{-m g R_{e}}{3}$
4 $\frac{-m g R_{e}}{4}$
BITSAT- 2005