If radius of earth is reduced by 1%, the escape velocity will (If mass of earth remains same):

Options

A. increase by 0.5%
B. decrease by 11%
C. no change
D. decrease by 5%

Answer

A

Explanation

`V_(e )=sqrt((2GM)/(R )), V_(e )^(.)= sqrt((2GM)/((99)/(100)R))`
% increase in escape velocity `=(V_(e)^(.)-V_(e ))/(V_(e )) xx 100`
`=(sqrt((200)/(99)-(GM)/(R ))-sqrt((2GM)/(R )))/(sqrt((2GM)/(R )))xx100=( sqrt((100)/(99))-1)xx100`
`=0.5%`
So, correct choice is (a).