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Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $= 6 \times 10^{24}\, kg$ and of the Sun $= 2 \times 10^{30}\, kg$. The average distance between the two is $1.5 \times 10^{11}\, m$.
$4.25 \times 10^{22} \,N$
$3.25 \times 10^{22} \,N$
$3.57 \times 10^{22} \,N$
$4.57 \times 10^{22} \,N$
Solution
According to the universal law of gravitation, the force of attraction between the Earth and the Sun is given by
$F=\frac{G \times M_{\text {Sun}} \times M_{\text {Earth}}}{R^{2}}$
Where,
$M_{Sun} =$ Mass of the Sun $= 2 \times 10^{30}\, kg$
$M_{Earth} =$ Mass of the Earth $= 6 \times 10^{24}\, kg$
$R = $ Average distance between the Earth and the Sun $= 1.5 \times 10^{11}\, m$
$G =$ Universal gravitational constant $= 6.7 \times 10^{-11}\, Nm^2\, kg^{-2}$
$F=\frac{6.7 \times 10^{-11} \times 2 \times 10^{30} \times 6 \times 10^{24}}{\left(1.5 \times 10^{11}\right)^{2}}=3.57 \times 10^{22} \,N$
Hence, the force of gravitation between the Earth and the Sun is $3.57 \times 10^{22} \,N$
