Question

The mass of a planet is twice and its radius is three times of the earth. The weight of a body, which has a mass of $5kg$, on that planet will be:

• A. $11.11N$
• B. $10.88N$
• C. $9.88N$
• D. $20.99N$

Answer 1

The correct option is B $10.88N$

Given:

The mass of the planet ($M_p$) = $2\times$ the mass of the earth ($M_e$)

The radius of the planet ($R_p$) = $3\times$ the radius of the earth ($R_e$)

The mass of the body $m=5kg$

The gravitational acceleration of the earth is $g=\frac{G{M}_e}{R_e^2}=9.8m/s^2$

The gravitational acceleration of the earth is $g^{\prime }=\frac{G{M}_p}{R_p^2}$

$\therefore \frac{g^{\prime }}{g}=\frac{M_p}{M_e}\times \frac{R_e^2}{R_p^2}=2\times \frac{1}{9}=\frac{2}{9}$

$\Rightarrow g^{\prime }=\frac{2g}{9}=\frac{2\times 9.8}{9}=2.18m/s^2$

The weight of the body of mass $5kg$ on the planet will be $W^{\prime }=m\times g^{\prime }=5\times 2.18=10.88N$