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Question

If mass and radius of the Earth are 6.0×1024 kg and 6.4×106 m respectively. Calculate the force exerted by the Earth on a body of mass 1 kg, acceleration of the body of mass 1 kg and acceleration of the Earth in order.
Use G=6.67×1011 Nm2kg2

A
9.8N
9.8 ms2
1 ms2
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B
9.8N
9.8 ms2
1.63×1024 ms2
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C
9.8N
1.63×1024 ms2
9.8 ms2
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D
9.8N
9.8 ms2
9.8 ms2
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Solution

The correct option is B 9.8N
9.8 ms2
1.63×1024 ms2
From Newton's law of gravitation, the force of attraction between the bodies is given by:
F=Gm1m2r2
Mass of Earth, m1=6.0×1024 kg
Mass of the body, m2=1 kg
Distance between the two bodies here is equal to the radius of earth.
r=6.4×106 m
Gravitational constant, G=6.67×1011 Nm2kg2

Substituting values, we get
F=6.67×1011×6.0×1024×1(6.4×106)2
F=9.8 N

Using newton's second law of motion, acceleration of the body is given by:
a2=Fm2
a2=9.8 N1 kg=9.8 ms2

Similarly, acceleration of the Earth is given by:
a1=Fm1
a1=9.8 N6.0×1024 kg
a1=1.63×1024 ms2

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