Question

If the mass of the planet is $10\%$ less than that of the earth and radius of the planet is $20\%$ greater than that of the earth the weight of 40 kg person on that planet is

• A. 10 kg wt
• B. 25 kg wt
• C. 40 kg wt
• D. 60 kg wt

Answer 1

The correct option is B 25 kg wt

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

Earth's gravity $g_e=\frac{G{M}_e}{{R_e}^2}\Rightarrow 1$

gravity on any planet$g_p=\frac{G{M}_p}{{R_p}^2}\Rightarrow 2$

$\frac{g_e}{g_p}=\frac{\frac{G{M}_e}{{R_e}^2}}{\frac{G{M}_p}{{R_P}^2}}$

$\frac{M_e}{M_p}=\frac{{R_p}^2}{{R_e}^2}$

$\frac{M_e}{0.9M_e}=\frac{{1.2}^2{R_e}^2}{{R_e}^2}$

$\frac{g_e}{g_p}=\frac{{1.2}^2}{0.9}=\frac{1.44}{0.9}=1.6⟹g_e=1.6g_p$

weight of the person on planet$=\frac{40}{1.6}=25kg$