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Question: The escape velocity for the earth is 11.2 km/sec. The mass of another planet is 100 times that of th...

The escape velocity for the earth is 11.2 km/sec. The mass of another planet is 100 times that of the earth and its radius is 4 times that of the earth. The escape velocity for this planet will be

A

112.0 km/s

B

5.6 km/s

C

280.0 km/s

D

56.0 km/s

Answer

56.0 km/s

Explanation

Solution

Escape velocity

v=2GMR⇒vpve=MpMe×ReRpv = \sqrt { \frac { 2 G M } { R } } \Rightarrow \frac { v _ { p } } { v _ { e } } = \sqrt { \frac { M _ { p } } { M _ { e } } \times \frac { R _ { e } } { R _ { p } } }

⇒vp=5ve=5×11.2=56 km/s\Rightarrow v _ { p } = 5 v _ { e } = 5 \times 11.2 = 56 \mathrm {~km} / \mathrm { s }