Question

The mass of a satellite is $\frac{M}{81}$ and radius is $\frac{R}{4}$ where $M$ and $R$ are the mass and radius of the planet. The satellite is revolving around the planet in an orbit of 5R. What will be the distance of the point from the surface of the planet, where the net force experienced will be zero?

• A. $4.8R$
• B. $6.5R$
• C. $2.8R$
• D. $3.8R$

Answer 1

The correct option is A $4.8R$

At null point,

$\frac{GMm}{(R+x{)}^2}=\frac{GMm}{81{(\frac{R}{4}+y)}^2}$
$R+x=9(\frac{R}{4}+y)$
$y=5R-x$
$R+x=9(\frac{R}{4}+5R-x)$
$4R+4x=189R-36x$
$40x=193R$
$x=4.825R$