1.

If the potential energy of body on a planet is numerically U and the escape velocity for the same body is v_(e ) for same planet then (U)/(v_(e )) will be :

Answer»

`m sqrt((GM)/(2R))`
`m sqrt((GM)/(R ))`
`m sqrt((2GM)/(R ))`
m`(GM)/(R )`

Solution :Potential ENERGY of body
`U=(GMm)/(R ) "" ` (NUMERICALLY)
Escape velocity is `v_(E )=sqrt((2GM)/(R )) `
`THEREFORE (U)/(v_(e ))=(GMm)/(R ) xx sqrt((R )/(2GM))`
`therefore (U)/(v_(e )) =m sqrt((GM)/(2R))`.
THUS correct choice is (a).


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