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The masses and radii of the earth and mo...

The masses and radii of the earth and moon are `(M_(1), R_(1))` and `(M_(2), R_(2))` respectively. Their centres are at a distance r apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :

A

`V=sqrt((4G(M_(1)+M_(2)))/(r))`

B

`V=(1)/(2)sqrt((2G(M_(1)+M_(2)))/(r))`

C

`V=(1)/(2)sqrt((4G(M_(1)+M_(2)))/(r))`

D

`V=(sqrt(2G)(M_(1)+M_(2)))/(r)`

Text Solution

Verified by Experts

The correct Answer is:
A

E = 0
`-((GM_(1))/(r//2)+(GM_(2))/(r//2))m+(1)/(2)mv_(e)^(2)=0`
`V_(e)=sqrt((4G(M_(1)+M_(2)))/(r))`
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