The escape velocity of a body from the Earth | vedclass

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(D) The formula for escape velocity is $V_e = \sqrt{\frac{2GM}{R}}$.Given for Earth: $V_E = 11.2 \,km/s$, $M_E$, and $R_E$.For the planet: $M_P = \fra

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$7.9$

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(D) The formula for escape velocity is $V_e = \sqrt{\frac{2GM}{R}}$.Given for Earth: $V_E = 11.2 \,km/s$, $M_E$, and $R_E$.For the planet: $M_P = \frac{M_E}{6}$ and $R_P = \frac{R_E}{3}$.The escape velocity for the planet is $V_P = \sqrt{\frac{2GM_P}{R_P}}$.Substituting the values: $V_P = \sqrt{\frac{2G(M_E/6)}{(R_E/3)}} = \sqrt{\frac{2GM_E}{R_E} 	imes \frac{3}{6}} = \sqrt{\frac{2GM_E}{R_E} 	imes \frac{1}{2}}$.Since $V_E = \sqrt{\frac{2GM_E}{R_E}} = 11.2 \,km/s$, we have $V_P = \frac{V_E}{\sqrt{2}}$.$V_P = \frac{11.2}{1.414} \approx 7.9 \,km/s$.

The escape velocity of a body from the Earth is $11.2 \,km/s$. If the radius of a planet is one-third the radius of the Earth and its mass is one-sixth that of the Earth, the escape velocity from the planet is: (in $\,km/s$)

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