Question

The mass and radius of earth is 'M_e' and 'R_e' respectively and that of moon is 'M_m' and 'R_m' respectively. The distance between the centre of the earth and that of moon is 'D'. The minimum speed required for a body (mass 'm') to project from a point midway between their centres to escape to infinity is ______.

Options

• `(G(M_e+M_m))/(2D)`

• `((GD)/M_e)^(1/2)`

• `2sqrt((G(M_e+M_m))/D)`

• `sqrt((M_e +M_m)/D)`

Answer 1

The mass and radius of earth is 'M_e' and 'R_e' respectively and that of moon is 'M_m' and 'R_m' respectively. The distance between the centre of the earth and that of moon is 'D'. The minimum speed required for a body (mass 'm') to project from a point midway between their centres to escape to infinity is `underline(2sqrt((G(M_e+M_m))/D))`.

Explanation:

Initial TE = Final TE

`-(GM_2m)/("d/2")-(GM_1m)/("d/2")=1/2"mv"^2`

`"v^2"=abs((4G)/d(M_1+M_2))`

`"v"=sqrt((4G(M_1+M_2))/d)=2sqrt((G(M_1+M_2))/d)`