Gravitational Potential
PHXI08:GRAVITATION

359892 The magnitude of \(P E\) of three objects of masses \(1\;kg,2\;kg\) and \(3\;kg\) placed at the three vertices of an equilateral triangle of side \(20\;cm\) is

1 \(25\,G\)
2 \(35\,G\)
3 \(45\,G\)
4 \(55\,G\)
PHXI08:GRAVITATION

359893 Let the minimum external work done in shifting a particle of mass \(m\) from centre of earth to earth's surface be \(W_{1}\) and that from surface of earth to inifinity be \(W_{2}\). Then \(\dfrac{W_{1}}{W_{2}}\) is equal to

1 \(1: 3\)
2 \(2: 1\)
3 \(1: 1\)
4 \(1: 2\)
PHXI08:GRAVITATION

359894 The gravitational field in a region is given by \(\vec g = 5\;N/kg\hat i + 12\;N/kg\hat j\). The change in the gravitational potential energy of a particle of mass 1 \(kg\) when it is taken from the origin to a point \((7 m,-3 m)\) is:

1 \(13 \sqrt{58} J\)
2 71\(J\)
3 \(1 J\)
4 \(-71 J\)
PHXI08:GRAVITATION

359895 A particle of mass \(10\;g\) is kept on the surface of a uniform sphere of mass \(100\;g\) and radius \(10\;cm\). Find the work to be done against the gravitational force between them, to take the particle far away from the sphere.
(Take, \(G = 6.67 \times {10^{ - 11}}N{m^2}\;k{g^{ - 2}}\))

1 \(13.34 \times {10^{ - 10}}\;J\)
2 \(3.33 \times {10^{ - 10}}\;J\)
3 \(6.67 \times {10^{ - 9}}\;J\)
4 \(6.67 \times {10^{ - 10}}\;J\)
PHXI08:GRAVITATION

359896 A particle is projected from point \(A\), that is at a distance 4\(R\) from the centre of the Earth, with speed \(v_{1}\) in a direction making \(30^{\circ}\) with the line joining the centre of the Earth and point \(A\), as shown. Find the speed \(v_{1}\) of particle (in \(m/s\)) if particle passes grazing the surface of the earth. Consider gravitational interaction only between earth and the particle.
(use \(\frac{{GM}}{R} = 6.4 \times {10^7}\;{m^2}/{s^2}\))
supporting img

1 800
2 \(\dfrac{8000}{\sqrt{2}}\)
3 \(800 \sqrt{2}\)
4 None of these
PHXI08:GRAVITATION

359892 The magnitude of \(P E\) of three objects of masses \(1\;kg,2\;kg\) and \(3\;kg\) placed at the three vertices of an equilateral triangle of side \(20\;cm\) is

1 \(25\,G\)
2 \(35\,G\)
3 \(45\,G\)
4 \(55\,G\)
PHXI08:GRAVITATION

359893 Let the minimum external work done in shifting a particle of mass \(m\) from centre of earth to earth's surface be \(W_{1}\) and that from surface of earth to inifinity be \(W_{2}\). Then \(\dfrac{W_{1}}{W_{2}}\) is equal to

1 \(1: 3\)
2 \(2: 1\)
3 \(1: 1\)
4 \(1: 2\)
PHXI08:GRAVITATION

359894 The gravitational field in a region is given by \(\vec g = 5\;N/kg\hat i + 12\;N/kg\hat j\). The change in the gravitational potential energy of a particle of mass 1 \(kg\) when it is taken from the origin to a point \((7 m,-3 m)\) is:

1 \(13 \sqrt{58} J\)
2 71\(J\)
3 \(1 J\)
4 \(-71 J\)
PHXI08:GRAVITATION

359895 A particle of mass \(10\;g\) is kept on the surface of a uniform sphere of mass \(100\;g\) and radius \(10\;cm\). Find the work to be done against the gravitational force between them, to take the particle far away from the sphere.
(Take, \(G = 6.67 \times {10^{ - 11}}N{m^2}\;k{g^{ - 2}}\))

1 \(13.34 \times {10^{ - 10}}\;J\)
2 \(3.33 \times {10^{ - 10}}\;J\)
3 \(6.67 \times {10^{ - 9}}\;J\)
4 \(6.67 \times {10^{ - 10}}\;J\)
PHXI08:GRAVITATION

359896 A particle is projected from point \(A\), that is at a distance 4\(R\) from the centre of the Earth, with speed \(v_{1}\) in a direction making \(30^{\circ}\) with the line joining the centre of the Earth and point \(A\), as shown. Find the speed \(v_{1}\) of particle (in \(m/s\)) if particle passes grazing the surface of the earth. Consider gravitational interaction only between earth and the particle.
(use \(\frac{{GM}}{R} = 6.4 \times {10^7}\;{m^2}/{s^2}\))
supporting img

1 800
2 \(\dfrac{8000}{\sqrt{2}}\)
3 \(800 \sqrt{2}\)
4 None of these
PHXI08:GRAVITATION

359892 The magnitude of \(P E\) of three objects of masses \(1\;kg,2\;kg\) and \(3\;kg\) placed at the three vertices of an equilateral triangle of side \(20\;cm\) is

1 \(25\,G\)
2 \(35\,G\)
3 \(45\,G\)
4 \(55\,G\)
PHXI08:GRAVITATION

359893 Let the minimum external work done in shifting a particle of mass \(m\) from centre of earth to earth's surface be \(W_{1}\) and that from surface of earth to inifinity be \(W_{2}\). Then \(\dfrac{W_{1}}{W_{2}}\) is equal to

1 \(1: 3\)
2 \(2: 1\)
3 \(1: 1\)
4 \(1: 2\)
PHXI08:GRAVITATION

359894 The gravitational field in a region is given by \(\vec g = 5\;N/kg\hat i + 12\;N/kg\hat j\). The change in the gravitational potential energy of a particle of mass 1 \(kg\) when it is taken from the origin to a point \((7 m,-3 m)\) is:

1 \(13 \sqrt{58} J\)
2 71\(J\)
3 \(1 J\)
4 \(-71 J\)
PHXI08:GRAVITATION

359895 A particle of mass \(10\;g\) is kept on the surface of a uniform sphere of mass \(100\;g\) and radius \(10\;cm\). Find the work to be done against the gravitational force between them, to take the particle far away from the sphere.
(Take, \(G = 6.67 \times {10^{ - 11}}N{m^2}\;k{g^{ - 2}}\))

1 \(13.34 \times {10^{ - 10}}\;J\)
2 \(3.33 \times {10^{ - 10}}\;J\)
3 \(6.67 \times {10^{ - 9}}\;J\)
4 \(6.67 \times {10^{ - 10}}\;J\)
PHXI08:GRAVITATION

359896 A particle is projected from point \(A\), that is at a distance 4\(R\) from the centre of the Earth, with speed \(v_{1}\) in a direction making \(30^{\circ}\) with the line joining the centre of the Earth and point \(A\), as shown. Find the speed \(v_{1}\) of particle (in \(m/s\)) if particle passes grazing the surface of the earth. Consider gravitational interaction only between earth and the particle.
(use \(\frac{{GM}}{R} = 6.4 \times {10^7}\;{m^2}/{s^2}\))
supporting img

1 800
2 \(\dfrac{8000}{\sqrt{2}}\)
3 \(800 \sqrt{2}\)
4 None of these
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PHXI08:GRAVITATION

359892 The magnitude of \(P E\) of three objects of masses \(1\;kg,2\;kg\) and \(3\;kg\) placed at the three vertices of an equilateral triangle of side \(20\;cm\) is

1 \(25\,G\)
2 \(35\,G\)
3 \(45\,G\)
4 \(55\,G\)
PHXI08:GRAVITATION

359893 Let the minimum external work done in shifting a particle of mass \(m\) from centre of earth to earth's surface be \(W_{1}\) and that from surface of earth to inifinity be \(W_{2}\). Then \(\dfrac{W_{1}}{W_{2}}\) is equal to

1 \(1: 3\)
2 \(2: 1\)
3 \(1: 1\)
4 \(1: 2\)
PHXI08:GRAVITATION

359894 The gravitational field in a region is given by \(\vec g = 5\;N/kg\hat i + 12\;N/kg\hat j\). The change in the gravitational potential energy of a particle of mass 1 \(kg\) when it is taken from the origin to a point \((7 m,-3 m)\) is:

1 \(13 \sqrt{58} J\)
2 71\(J\)
3 \(1 J\)
4 \(-71 J\)
PHXI08:GRAVITATION

359895 A particle of mass \(10\;g\) is kept on the surface of a uniform sphere of mass \(100\;g\) and radius \(10\;cm\). Find the work to be done against the gravitational force between them, to take the particle far away from the sphere.
(Take, \(G = 6.67 \times {10^{ - 11}}N{m^2}\;k{g^{ - 2}}\))

1 \(13.34 \times {10^{ - 10}}\;J\)
2 \(3.33 \times {10^{ - 10}}\;J\)
3 \(6.67 \times {10^{ - 9}}\;J\)
4 \(6.67 \times {10^{ - 10}}\;J\)
PHXI08:GRAVITATION

359896 A particle is projected from point \(A\), that is at a distance 4\(R\) from the centre of the Earth, with speed \(v_{1}\) in a direction making \(30^{\circ}\) with the line joining the centre of the Earth and point \(A\), as shown. Find the speed \(v_{1}\) of particle (in \(m/s\)) if particle passes grazing the surface of the earth. Consider gravitational interaction only between earth and the particle.
(use \(\frac{{GM}}{R} = 6.4 \times {10^7}\;{m^2}/{s^2}\))
supporting img

1 800
2 \(\dfrac{8000}{\sqrt{2}}\)
3 \(800 \sqrt{2}\)
4 None of these
PHXI08:GRAVITATION

359892 The magnitude of \(P E\) of three objects of masses \(1\;kg,2\;kg\) and \(3\;kg\) placed at the three vertices of an equilateral triangle of side \(20\;cm\) is

1 \(25\,G\)
2 \(35\,G\)
3 \(45\,G\)
4 \(55\,G\)
PHXI08:GRAVITATION

359893 Let the minimum external work done in shifting a particle of mass \(m\) from centre of earth to earth's surface be \(W_{1}\) and that from surface of earth to inifinity be \(W_{2}\). Then \(\dfrac{W_{1}}{W_{2}}\) is equal to

1 \(1: 3\)
2 \(2: 1\)
3 \(1: 1\)
4 \(1: 2\)
PHXI08:GRAVITATION

359894 The gravitational field in a region is given by \(\vec g = 5\;N/kg\hat i + 12\;N/kg\hat j\). The change in the gravitational potential energy of a particle of mass 1 \(kg\) when it is taken from the origin to a point \((7 m,-3 m)\) is:

1 \(13 \sqrt{58} J\)
2 71\(J\)
3 \(1 J\)
4 \(-71 J\)
PHXI08:GRAVITATION

359895 A particle of mass \(10\;g\) is kept on the surface of a uniform sphere of mass \(100\;g\) and radius \(10\;cm\). Find the work to be done against the gravitational force between them, to take the particle far away from the sphere.
(Take, \(G = 6.67 \times {10^{ - 11}}N{m^2}\;k{g^{ - 2}}\))

1 \(13.34 \times {10^{ - 10}}\;J\)
2 \(3.33 \times {10^{ - 10}}\;J\)
3 \(6.67 \times {10^{ - 9}}\;J\)
4 \(6.67 \times {10^{ - 10}}\;J\)
PHXI08:GRAVITATION

359896 A particle is projected from point \(A\), that is at a distance 4\(R\) from the centre of the Earth, with speed \(v_{1}\) in a direction making \(30^{\circ}\) with the line joining the centre of the Earth and point \(A\), as shown. Find the speed \(v_{1}\) of particle (in \(m/s\)) if particle passes grazing the surface of the earth. Consider gravitational interaction only between earth and the particle.
(use \(\frac{{GM}}{R} = 6.4 \times {10^7}\;{m^2}/{s^2}\))
supporting img

1 800
2 \(\dfrac{8000}{\sqrt{2}}\)
3 \(800 \sqrt{2}\)
4 None of these