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Assuming earth as a uniform sphere of ra...

Assuming earth as a uniform sphere of radius R, if we project a body along the smooth diametrical chute form the centre of earth with a speed v such that it will just reach the earth's surface then v is equal to :

A

`sqrt(gR)`

B

`sqrt(2gR)`

C

`sqrt((gR)/2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(KE+PE)_(1)=(KE+PE)_(2)`
`1/2mv^(2)-3/2(GMm)/R=-(GMm)/R`
`v=sqrt((GM)/R)=sqrt((gR^(2))/R) =sqrt(gR)`
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