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The masses and radii of the earth an moo...

The masses and radii of the earth an moon are `M_(1) and R_(1) and M_(2), R_(2)` respectively. Their centres are at a distacne r apart. Find the minimum speed with which the particle of mass m should be projected from a point mid-way between the two centres so as to escape to infinity.

A

`sqrt((4G)/(r)(M_(e)+M_(m)))`

B

`(4G)/(r)sqrt((M_(e)+M_(m)))`

C

`sqrt((2G)/(r)(M_(e)+M_(m)))`

D

`(2G)/(r)sqrt((M_(e)+M_(m)))`

Text Solution

Verified by Experts

The correct Answer is:
A

`u_(i)+k_(i)=u_(i)+k_(f)`
`(GmM^(E))/(r//2)-(GmM_(M))/(r//2)+1/2mv^(2)=0`
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Knowledge Check

  • The radii of a planet and its satellite are 2r and r and their densities are rho and 2rho respectively. Their centres are separated by a distance d. The minimum speed with which a body should be projected from the mid point of the line joining their centres so that the body escapes to infinity is (G-universal gravitational constant)

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    `4[sqrt((10Gpir^3rho)/(3d))]`
    B
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