1.

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

Answer»

INCREASE by 0.5%
decrease by 11%
no change
decrease by 5%

Solution :`V_(e )=sqrt((2GM)/(R )), V_(e )^(.)= sqrt((2GM)/((99)/(100)R))`
% INCREASEIN 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).


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