Question

The rail of a planet and its satellite are $2r$ and their densities are P and $2p$ respectively.Their centres are separated by a distance d. The ratio of minimum speed with which a body should be projected from the midpoint

• A. $1:1$
• B. $2:1$
• C. $3:2$
• D. $2:3$

Answer 1

The correct option is A $1:1$

Acc due to gravity at the surface of planet $=g=\left(4/3\right)GR\lambda p$
Planet $1;R=R$
$p=P$
so,

$g_1=\frac{4}{3}GRP\lambda$
planet $2;R=2R$
$p=\frac{P}{2}$
so,
$g_1=\frac{4}{3}GRP\times \frac{\lambda }{2}$
or
$g2=\frac{4}{3}GR\lambda P$
thus $g1=g2$
ratio will be $1:1$