Earth Satellites
PHXI08:GRAVITATION

359715 The ratio of energy required to raise a satellite of mass \(m\) to a height \(h\) above the earth's surface of that required to put it into the orbit at same height is (\(R=\) radius of earth)

1 \(\dfrac{h}{R}\)
2 \(\dfrac{3 h}{R}\)
3 \(\dfrac{4 h}{R}\)
4 \(\dfrac{2 h}{R}\)
PHXI08:GRAVITATION

359716 A satellite of mass \(m\) is launched vertically upwards with an initial speed \(u\) from the surface of the earth. After it reaches height \(R(R = \) radius of the earth), it ejects a rocket of mass \(\dfrac{m}{10}\) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is \((G\) is the gravitational constant; \(M\) is the mass of the earth) :

1 \(5 m\left(u^{2}-\dfrac{119}{200} \dfrac{G M}{R}\right)\)
2 \(\dfrac{m}{20}\left(u-\sqrt{\dfrac{2 G M}{R}}\right)^{2}\)
3 \(\dfrac{3 m}{8}\left(u+\sqrt{\dfrac{5 G M}{6 R}}\right)^{2}\)
4 \(\dfrac{m}{20}\left(u^{2}+\dfrac{113}{200} \dfrac{G M}{R}\right)\)
PHXI08:GRAVITATION

359717 A satellite \(S\) is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth:

1 The acceleration of \(S\) is always directed towards the centre of the earth.
2 The angular momentum of \(S\) about the centre of the earth changes in direction, but its magnitude remains constant.
3 The total mechanical energy of \(S\) varies periodically with time.
4 The linear momentum of \(S\) remains constant in magnitude.
PHXI08:GRAVITATION

359718 An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5\,km\) . From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \dfrac{G M_{e} m}{21 R_{e}}\). The value of \(x\) is
(take \({R_e} = 6370\;km\) )

1 9
2 12
3 10
4 11
PHXI08:GRAVITATION

359715 The ratio of energy required to raise a satellite of mass \(m\) to a height \(h\) above the earth's surface of that required to put it into the orbit at same height is (\(R=\) radius of earth)

1 \(\dfrac{h}{R}\)
2 \(\dfrac{3 h}{R}\)
3 \(\dfrac{4 h}{R}\)
4 \(\dfrac{2 h}{R}\)
PHXI08:GRAVITATION

359716 A satellite of mass \(m\) is launched vertically upwards with an initial speed \(u\) from the surface of the earth. After it reaches height \(R(R = \) radius of the earth), it ejects a rocket of mass \(\dfrac{m}{10}\) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is \((G\) is the gravitational constant; \(M\) is the mass of the earth) :

1 \(5 m\left(u^{2}-\dfrac{119}{200} \dfrac{G M}{R}\right)\)
2 \(\dfrac{m}{20}\left(u-\sqrt{\dfrac{2 G M}{R}}\right)^{2}\)
3 \(\dfrac{3 m}{8}\left(u+\sqrt{\dfrac{5 G M}{6 R}}\right)^{2}\)
4 \(\dfrac{m}{20}\left(u^{2}+\dfrac{113}{200} \dfrac{G M}{R}\right)\)
PHXI08:GRAVITATION

359717 A satellite \(S\) is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth:

1 The acceleration of \(S\) is always directed towards the centre of the earth.
2 The angular momentum of \(S\) about the centre of the earth changes in direction, but its magnitude remains constant.
3 The total mechanical energy of \(S\) varies periodically with time.
4 The linear momentum of \(S\) remains constant in magnitude.
PHXI08:GRAVITATION

359718 An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5\,km\) . From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \dfrac{G M_{e} m}{21 R_{e}}\). The value of \(x\) is
(take \({R_e} = 6370\;km\) )

1 9
2 12
3 10
4 11
PHXI08:GRAVITATION

359715 The ratio of energy required to raise a satellite of mass \(m\) to a height \(h\) above the earth's surface of that required to put it into the orbit at same height is (\(R=\) radius of earth)

1 \(\dfrac{h}{R}\)
2 \(\dfrac{3 h}{R}\)
3 \(\dfrac{4 h}{R}\)
4 \(\dfrac{2 h}{R}\)
PHXI08:GRAVITATION

359716 A satellite of mass \(m\) is launched vertically upwards with an initial speed \(u\) from the surface of the earth. After it reaches height \(R(R = \) radius of the earth), it ejects a rocket of mass \(\dfrac{m}{10}\) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is \((G\) is the gravitational constant; \(M\) is the mass of the earth) :

1 \(5 m\left(u^{2}-\dfrac{119}{200} \dfrac{G M}{R}\right)\)
2 \(\dfrac{m}{20}\left(u-\sqrt{\dfrac{2 G M}{R}}\right)^{2}\)
3 \(\dfrac{3 m}{8}\left(u+\sqrt{\dfrac{5 G M}{6 R}}\right)^{2}\)
4 \(\dfrac{m}{20}\left(u^{2}+\dfrac{113}{200} \dfrac{G M}{R}\right)\)
PHXI08:GRAVITATION

359717 A satellite \(S\) is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth:

1 The acceleration of \(S\) is always directed towards the centre of the earth.
2 The angular momentum of \(S\) about the centre of the earth changes in direction, but its magnitude remains constant.
3 The total mechanical energy of \(S\) varies periodically with time.
4 The linear momentum of \(S\) remains constant in magnitude.
PHXI08:GRAVITATION

359718 An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5\,km\) . From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \dfrac{G M_{e} m}{21 R_{e}}\). The value of \(x\) is
(take \({R_e} = 6370\;km\) )

1 9
2 12
3 10
4 11
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PHXI08:GRAVITATION

359715 The ratio of energy required to raise a satellite of mass \(m\) to a height \(h\) above the earth's surface of that required to put it into the orbit at same height is (\(R=\) radius of earth)

1 \(\dfrac{h}{R}\)
2 \(\dfrac{3 h}{R}\)
3 \(\dfrac{4 h}{R}\)
4 \(\dfrac{2 h}{R}\)
PHXI08:GRAVITATION

359716 A satellite of mass \(m\) is launched vertically upwards with an initial speed \(u\) from the surface of the earth. After it reaches height \(R(R = \) radius of the earth), it ejects a rocket of mass \(\dfrac{m}{10}\) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is \((G\) is the gravitational constant; \(M\) is the mass of the earth) :

1 \(5 m\left(u^{2}-\dfrac{119}{200} \dfrac{G M}{R}\right)\)
2 \(\dfrac{m}{20}\left(u-\sqrt{\dfrac{2 G M}{R}}\right)^{2}\)
3 \(\dfrac{3 m}{8}\left(u+\sqrt{\dfrac{5 G M}{6 R}}\right)^{2}\)
4 \(\dfrac{m}{20}\left(u^{2}+\dfrac{113}{200} \dfrac{G M}{R}\right)\)
PHXI08:GRAVITATION

359717 A satellite \(S\) is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth:

1 The acceleration of \(S\) is always directed towards the centre of the earth.
2 The angular momentum of \(S\) about the centre of the earth changes in direction, but its magnitude remains constant.
3 The total mechanical energy of \(S\) varies periodically with time.
4 The linear momentum of \(S\) remains constant in magnitude.
PHXI08:GRAVITATION

359718 An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5\,km\) . From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \dfrac{G M_{e} m}{21 R_{e}}\). The value of \(x\) is
(take \({R_e} = 6370\;km\) )

1 9
2 12
3 10
4 11