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(D) The formula for escape velocity is $v_e = \sqrt{\frac{2GM}{R}}$.Given values are $M = 6 	imes 10^{24} \ kg$,$v_e = 3 	imes 10^8 \ m/s$,and $G =

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$9 \ mm$

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(D) The formula for escape velocity is $v_e = \sqrt{\frac{2GM}{R}}$.Given values are $M = 6 	imes 10^{24} \ kg$,$v_e = 3 	imes 10^8 \ m/s$,and $G = 6.67 	imes 10^{-11} \ N \cdot m^2/kg^2$.Squaring both sides,we get $v_e^2 = \frac{2GM}{R}$.Rearranging for $R$,we get $R = \frac{2GM}{v_e^2}$.Substituting the values: $R = \frac{2 	imes 6.67 	imes 10^{-11} 	imes 6 	imes 10^{24}}{(3 	imes 10^8)^2}$.$R = \frac{80.04 	imes 10^{13}}{9 	imes 10^{16}} = 8.893 	imes 10^{-3} \ m \approx 9 	imes 10^{-3} \ m$.Since $1 \ mm = 10^{-3} \ m$,the radius is $9 \ mm$.

$A$ mass of $6 \times 10^{24} \ kg$ is to be compressed into a sphere in such a way that the escape velocity from the sphere is $3 \times 10^8 \ m/s$. What should be the radius of the sphere? (Given: $G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$)

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