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Question
What is the force of gravity on a body of mass 150 kg lying on the surface of the earth? (Mass of earth = 6 x 1024 kg; Radius of earth = 6.4 x 106 m; G = 6.7 x 10-11 Nm2/kg2)
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Solution
F (gravitational force) = ?
G (gravitational constant) = 6.7 × 10−11 Nm2 kg−2
M (mass of earth)= 6 × 1024 kg
m (mass of body) = 150 kg
r (radius of earth) = 6.4 × 106 m
`F = (GMm)/r^2`
= `(6.7 xx 10^-11 xx 6 xx 10^24 xx 150)/(6.4 xx 10^6)^2`
= `(6.7 xx 10^-11 xx 6 xx 10^24 xx 150)/(6.4 xx 6.4 xx 10^12)` (`10^(24-11) = 10^13`)
= `(6.7 xx 6 xx 15 xx 10^14)/(6.4 xx 6.4 xx 10^12)` (`10^(14-12)=10^2`)
= `14.72 xx 10^2`
= 1472 N
Answer : Force of gravity = 1,472 N
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