Question

A body weights $3.5$ kg wt. on the surface of the earth. What will be its weight on the surface of a planet whose mass is $\frac{1}{7}$th of the mass of the earth and radius half of that of the earth?

Answer 1

Mass of body on earth =3.5 kg

Weight of the body on earth $W_E=mg=m\frac{G{M}_E}{R_E^2}$.

Where G=gravitational constant ,M= mass of Earth and R=radius of earth

Now weight of the body on the planet $W_P=m{g}_P=m\frac{G{M}_P}{R_P^2}$

As mass remains constant we can equate for acceleration due to gravity of the planet

$\frac{g_P}{g_P}=\frac{\frac{G{M}_P}{R_P^2}}{\frac{G{M}_E}{R_E^2}}$--------(A)

As mass of planet $M_P=\frac{1}{7}{M}_E$ and radius of planet $R_P=\frac{1}{2}{R}_E$

Putting the above values in A we get

$\frac{g_P}{g_E}=\frac{\frac{G\frac{1}{7}{M}_E}{\frac{1}{4}{R}_E^2}}{\frac{G{M}_E}{R_E^2}}{g}_P=\frac{4}{7}{g}_E=\frac{40}{7}$

Now weight of the body on the planet $W_P=mg$

$W_P=3.5\times \frac{40}{7}=20N$