Question

Two solid spherical planets of equal radii R having masses 4 M and 9 M their centre are separated by a distance 6 R. A projectile of mass m is sent from the planet of mass 4 M towards the havier planet. what is the distance r of the point from the lighter planet where the gravitational force on the projectile is zero?

• A. $1.4R$
• B. $1.8R$
• C. $1.5R$
• D. $2.4R$

Answer 1

Answer: (D)

$2.4R$

At null point ,

$F_{4M,m}=F_{9M,m}$ $(\therefore F=\frac{G{m}_1{m}_2}{d^2})$

$\frac{G4Mm}{r^2}=\frac{G9Mm}{(6R-r{)}^2}$

$\frac{4}{r^2}=\frac{9}{(6R-r{)}^2}$

$\frac{2}{r}=\frac{3}{(6R-r)}$

$12R-2r=3r$

$5r=12R$

$r=\frac{12}{5}R$

$r=2.4R$