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What is the required velocity for an atm...

What is the required velocity for an atmospheric particle 2000 km above the earth's surface to escape its gravitational pull? (Radius of the earth `= 6.4 xx 10^(6)" m and "g = 10 ms^(-2)`)

A

`9.68 kms^(-1)`

B

`9.78kms^(-1)`

C

`9.88kms^(-1)`

D

`9.98kms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Escape velocity `v_(e )=sqrt(2gR)`
At a height h above the Earth.s surface,
`v_(e )= sqrt(2g_(h) (R +h))` and
`g_(h)=(gR^(2))/((R+h)^(2)) :.v_(e )=sqrt((2gR^(2))/((R+h)^(2))(R+h))`
`=sqrt((2gR^(2))/((R+h)))`
`=sqrt((2xx10xx(6.4xx10^(6))^(2))/((6.4+2)10^(6)))`
`=sqrt((2 xx 10xx 6.4^(2) xx 10^(12))/(8.4 xx 10^(5)))`
`=sqrt((20xx40.96)/(8.4))=9.88km//s`
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