Question

What is the magnitude of a gravitational force between the earth and a 1 kg object on its surface if mass of Earth is 6 into 10 ki power 24 kg and radius of earth is 6.4 into 10 ki power 6 metre?​

Answer 1

${\frak{Given}} \begin{cases} & \text{Mass of body, m = 1 kg } \\ & \text{Mass of the earth, M = \sf 6 \times 10^{24} kg } \\ & \text{Radius of the earth, R = \sf 6.4 \times 10^6 m } \end{cases}$

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☯ We have to find, Magnitude of gravitational force

between the earth and surface of object.

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

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Magnitude of the gravitational force (F) between the earth and the body can be given as,

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$\star\;{\boxed{\sf{\pink{F = \dfrac{GMm}{R^2}}}}}$

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where,

F = Force between earth and body

G = Gravitational constant

M = Mass of earth

m = Mass object

R = Radius of earth

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$\dag\;{\underline{\frak{Now,\;Putting\;values,}}}$

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$:\implies\sf \dfrac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 1}{(6.4 \times 10^6)^2}$

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$:\implies\sf \dfrac{6.67 \times 6 \times 10}{6.4 \times 6.4}$

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$:\implies{\underline{\boxed{\sf{\pink{9.8\;N\;(approx)}}}}}\;\bigstar$

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∴ The magnitude of gravitational force between the earth and the body is 9.8 N.