The mass of the sun is 2 x 10³⁰kg and the mass of the earth is 6 x 10²⁴ kg. If the average distance between the sun and the earth is 1.5 x 10⁸ km, calculate the force of gravitation between them. G=6.7 x 10^-11 Nm² kg ^-2.

Academic Physics NCERT Class 9

Given:

$G($ gravitational constant $)=6.673 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{-2}$

$\mathrm{M}($ mass of sun $)=2 \times 10^{30} \mathrm{kg}$

$m($ mass of earth $)=6 \times 10^{24} \mathrm{kg}$

To find: We have to find the force of gravitation between the earth and the sun.

Solution:

We know Gravitational force between two objects $F=\frac{G M m}{d^{2}}$

d (distance between sun and earth) $=1.5 \times 10^{8} \mathrm{km}=1.5 \times 10^{8} \times 1000=1.5 \times10^{11} \mathrm{m}$

$=\frac{6.673 \times 10^{-11} \times 2 \times 10^{30} \times 6 \times 10^{24}}{\left(1.5 \times 10^{11}\right)^{2}}$

$=\frac{6.673 \times 10^{-11} \times 2 \times 10^{30} \times 6 \times 10^{24}}{1.5 \times 1.5\times10^{22}}$

$=\frac{6.673 \times 2 \times 6 \times 10^{43}}{1.5 \times 1.5 \times 10^{22}} $

$=\frac{6.673 \times 2 \times 6 \times 10^{21}}{1.5 \times 1.5}$

$=\frac{80.076 \times 10^{21}}{1.5 \times 1.5}$

$=35.59 \times 10^{21} N=3.57 \times 10^{22} N$

Answer : Gravitational Force $=3.57 \times 10^{22} \mathrm{N}$

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Updated on: 10-Oct-2022

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