Question

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth's surface is 11 km s^-1 , the escape velocity from the surface of the planet would be ______. 

Options

• 1.1 km s^-1

• 11 km s^-1

• 110 km s^-1

• 0.11 km s^-1

Answer 1

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth's surface is 11 km s^-1, the escape velocity from the surface of the planet would be 110 km s^-1. 

Explanation:

`("v"_"e")_"p"/("v"_"e")_"e" = sqrt((2"GM"_"p")/"R"_"p")/sqrt((2"GM"_"e")/"R"_"e")`

= `sqrt("M"_"p"/"M"_"e"xx"R"_"e"/"R"_"p")`

= `sqrt((10"M"_"e")/"M"_"e"xx"R"_"e"/("R"_"e"//10)`

= 10

∴ (v_e)_p = 10 × (v_e)_e 

= 10 × 11

= 110 km/s