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Question

The mass of planet Jupiter is 1.9×1027kg and that of the Sun is 1.99×1030kg. The mean distance of Jupiter from the Sun is 7.8×1011m. Calculate the gravitational force which Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also calculate the speed of Jupiter. G=6.67×1011 Nm2kg2.

A
=5×1023N
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B
=4.15×1023N
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C
=15×1023N
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D
=1×1023N
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Solution

The correct option is B. =4.15×1023N.

Mass of Jupiter=1.9×1027=M1
Mass of Sun=1.99×1030=M2
Mean distance of Jupiter from Sun=7.8×1011m=r
G=6.67×1011N2
Gravitational Force, F=GM1M2r2
F=6.67×1011×1.9×1027×1.99×1030(7.8×1011)2
F=4.16×1023N


Let the orbital speed of the jupiter be v.

The necessary centripetal force required to move in a circular orbit is provided by the gravitational pull acting on the jupiter.

Therefore, Centripetal force = Gravitational force

mv2r=F

v=Frm

v=4.16×1023×7.8×10111.9×1027

v=1.3×104 m/s.


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