Question

If the mass of the earth is $80$ times of that of planet and diameter is double that of planet and $g$ on earth $9.8m/s^2$ . Then, the value of $g$ on the planet will be

• A. $0.49m/s^2$
• B. $4.9m/s^2$
• C. $0.98m/s^2$
• D. $9.8m/s^2$

Answer 1

Answer: (A)

Mass of the earth $M_e=80M_p$ Diameter of earth $D_e=2D_p$ or radius of the earth $R_e=2R_p$ Gravitational acceleration is $g=\frac{GM}{R^2}\propto \frac{M}{R^2}$ or $\frac{g_e}{g_p}=\frac{M_e}{M_p}\times {\left(\frac{R_p}{R_e}\right)}^2$ $\frac{g_e}{g_p}=\frac{80M_p}{M_p}\times {\left(\frac{R_p}{2R_p}\right)}^2=80\times \frac{1}{4}=20$ So, $g_p=\frac{g_e}{20}=\frac{9.8}{20}=0.49m/s^2$