1.

Two masses m_(1) and m_(2) are initially at rest at infinite distance. They approach each other due to gravitational attraction. What is the speed of approach at a distance r between them?

Answer»

`(2G)/(r(m_(1)+m_(2)))`
`[(2G(m_(1)+m_(2)))/(r )]^((1)/(2))`
`((2Gr)/(m_(1)+m_(2)))^((1)/(2))`
`((2Gr)/(m_(1)+m_(2)))`.

Solution :When MASSES are infinite distance apart then their K.E, P.E and hence total energyis zero.
If v is the relative VELOCITY of approach then by LAW of CONSERVATION of energy.
`(1)/(2) ((m_(1)m_(2))/(m_(1)+m_(2)))v^(2)-(Gm_(1)m_(2))/(r )=0`
or `v=[(2G(m_(1)+m_(2)))/(r )]^((1)/(2))`
Thus correct CHOICE is (b).


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