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v(e )and v(p) denote the escape velociti...

`v_(e )`and `v_(p)` denote the escape velocities from the earth and another planet having twice the radius and the same mean density as that of the earth. Then

A

`v_(e )v_(p)//2`

B

`v_(e )=v_(p)`

C

`v_(e )=2v_(p)`

D

`v_(e )=(p)/(4)`.

Text Solution

Verified by Experts

The correct Answer is:
A
Escape velocity `v_(e )=sqrt((2GM)/(R ))`
`=sqrt((2G)/(R )xx((4)/(3)piR^(3))rho)=sqrt((8piGrho)/(3))R`.
`:. (v_(e ))/(v_(p))=(R )/(2R )=(1)/(2)`.
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