A body shows a weight 90 kg on a weighing machine on the earth’s surface. The mass of one of the moons in a solar system is$\frac{1}{9}$ that of the earth’s mass and its radius is$\frac{1}{2}$ that of the earth’s radius. The weighing machine will show the weight of the body on the moon as

The weight of the body depends on the gravitational force exerted on the body.
When an object is kept on a weighing machine, it exerts a force on the weighing machine. The force depends on the acceleration due to gravity.

Accelraation due to gravity is given by:

$g=\frac{GM}{R^2}$

$\frac{{\text{g}}_{\text{m}}}{{\text{g}}_{\text{e}}}=\frac{{\text{M}}_{\text{m}}}{{\text{M}}_{\text{e}}}\times {\left(\frac{{\text{R}}_{\text{e}}}{{\text{R}}_{\text{m}}}\right)}^{\text{2}}$ 

$=\frac{1}{9}\times {\left(\frac{2}{1}\right)}^2=\frac{4}{9}$

${\text{g}}_{\text{m}}=\frac{4}{9}{\text{g}}_{\text{e}}$

${\text{w}}_{\text{m}}=\frac{4}{9}\times {\text{w}}_{\text{e}}$

$\frac{4}{9}\times 90=40\text{kg}$