The mass of the earth is 6.00 times 10^{24} | vedclass

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Question

(A) The gravitational potential energy $U$ of a system of two masses $M$ and $m$ separated by a distance $r$ is given by the formula: $U = -\frac{GMm}

Vedclass · Accepted Answer

$3.80 	imes 10^8 \ m$

Vedclass · Answer

(A) The gravitational potential energy $U$ of a system of two masses $M$ and $m$ separated by a distance $r$ is given by the formula: $U = -\frac{GMm}{r}$.Given:$M = 6.00 	imes 10^{24} \ kg$$m = 7.40 	imes 10^{22} \ kg$$G = 6.67 	imes 10^{-11} \ N \cdot m^2/kg^2$$U = -7.79 	imes 10^{28} \ J$Rearranging the formula to solve for $r$:$r = -\frac{GMm}{U}$Substituting the values:$r = \frac{6.67 	imes 10^{-11} 	imes 6.00 	imes 10^{24} 	imes 7.40 	imes 10^{22}}{7.79 	imes 10^{28}}$$r = \frac{296.196 	imes 10^{35}}{7.79 	imes 10^{28}}$$r \approx 38.02 	imes 10^7 \ m = 3.80 	imes 10^8 \ m$.

The mass of the earth is $6.00 \times 10^{24} \ kg$ and that of the moon is $7.40 \times 10^{22} \ kg$. The gravitational constant is $G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$. The potential energy of the system is $-7.79 \times 10^{28} \ J$. The mean distance between the earth and the moon is:

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