The mass of the moon is 7.34 times 10^{22} k | vedclass

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(B) The formula for acceleration due to gravity on the surface of a celestial body is given by $g = \frac{GM}{R^2}$,where $G$ is the gravitational con

Vedclass · Accepted Answer

$1.87 	imes 10^6 \ m$

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(B) The formula for acceleration due to gravity on the surface of a celestial body is given by $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass,and $R$ is the radius.Rearranging the formula to solve for the radius $R$,we get $R = \sqrt{\frac{GM}{g}}$.Substituting the given values: $G = 6.667 	imes 10^{-11} \ N \cdot m^2/kg^2$,$M = 7.34 	imes 10^{22} \ kg$,and $g = 1.4 \ m/s^2$.$R = \sqrt{\frac{6.667 	imes 10^{-11} 	imes 7.34 	imes 10^{22}}{1.4}}$$R = \sqrt{\frac{48.93578 	imes 10^{11}}{1.4}}$$R = \sqrt{34.954 	imes 10^{11}} = \sqrt{3.4954 	imes 10^{12}}$$R \approx 1.87 	imes 10^6 \ m$.

The mass of the moon is $7.34 \times 10^{22} \ kg$. If the acceleration due to gravity on the moon is $1.4 \ m/s^2$,calculate the radius of the moon. (Given: $G = 6.667 \times 10^{-11} \ N \cdot m^2/kg^2$)

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