22. A rocket is fired from the earth towards the Sun. At
what distance from the ear5th's centre is the
gravitational force on the rocket zero? (Mass of the
sun - 2 x 10 kg, mass of the earth = 1.5 x 10"m).
(a) x-26 x 10 km (b)x=2.6 x 10 km
(c)x -2.6 x 104 km (d) x -2.6 x 10 km
Answers
Answered by
1
Explanation:
Mass of the Sun, M
s
=2×10
30
kg
Mass of the Earth, M
e
=6×10
24
kg
Orbital radius, r=1.5×10
11
m
Mass of the rocket =m
Let x be the distance from the centre of the Earth where the gravitational force acting on satellite P becomes zero.
From Newton’s law of gravitation, we can equate gravitational forces acting on satellite P under the influence of the Sun and the Earth as:
(r−x)
2
GmM
s
=
x
2
GmM
e
[
x
(r−x)
]
2
=M
s
/M
e
(r−x)/x=(
60×10
24
2×10
30
)
1/2
=577.35
1.5×10
11
−x=577.35x
578.35x=1.5×10
11
x=1.5×10
11
/578.35=2.59×10
8
m.
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