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Standard IX

Physics

Gravitational Force

An earth like...

Question

An earth like planet has a mass $6$ times and radius twice that of the earth. If the escape speed of a body at rest on the earth surface is $v_{e +}$ that from the planet is?

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Solution

$V_{e} = \sqrt{\frac{2 G M_{e}}{R_{e}}}$

$M = 6 M_{e}$

$R = 2 R_{e}$

$\frac{v}{V_{e}} = \frac{\sqrt{\frac{2 G M}{R}}}{\sqrt{\frac{2 G M_{e}}{R_{e}}}} = \sqrt{3}$

$v = \sqrt{3} V_{e}$

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An earth like planet has a mass 6 times and radius twice that of the earth. If the escape speed of a body at rest on the earth surface is ve+ that from the planet is?

Ve=√2GMeReM=6MeR=2RevVe=√2GMR√2GMeRe=√3v=√3Ve

An earth like planet has a mass $6$ times and radius twice that of the earth. If the escape speed of a body at rest on the earth surface is $v_{e +}$ that from the planet is?

$V_{e} = \sqrt{\frac{2 G M_{e}}{R_{e}}}$

$M = 6 M_{e}$

$R = 2 R_{e}$

$\frac{v}{V_{e}} = \frac{\sqrt{\frac{2 G M}{R}}}{\sqrt{\frac{2 G M_{e}}{R_{e}}}} = \sqrt{3}$

$v = \sqrt{3} V_{e}$