Question 244: Gravitation

Question

Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $$\sqrt {{a \over 7}{{GM} \over R}} $$ then the value of 'a' is ____________.
[Given : The two planets are fixed in their position]

Accepted Answer

Acceleration due to gravity will be zero at P therefore,
$${1 \over 2}m{v^2} - {{GMm} \over R} - {{G9Mm} \over {7R}} = 0 - {{GMm} \over {2R}} - {{G9Mm} \over {6R}}$$
$$	herefore$$ $$V = \sqrt {{4 \over 7}{{GM} \over R}} $$

Gravitation

Integer / Numeric Answer Type