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If v(e) is escape velocity and v(0), is ...

If `v_(e)` is escape velocity and `v_(0)`, is orbital velocity of satellite for orbit close to the earth's surface. Then are related by

A

`v_(o)=sqrt(2)v_(e )`

B

`v_(o)=v_(e )`

C

`v_(e )=(v_(o))/(2)`

D

`v_(e )=sqrt(2)v_(o)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) Escape velocity , `v_(e)=sqrt((2GM_(E))/(R_(E)))` …(i)
where `M_(E) " and " R_(E)` be the mass and radius of the earth respectively.
The orbital velocity of a satellite close to the earth's surface is
`v_(o)=sqrt((GM_(E))/(R ))`
From (i) and (ii), we get `v_(e)=sqrt(2)v_(o)`..... .. (ii)
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