Question

if a mass of a planet is 10% less than that of earth and the radius 20% greater than that of earth the acceleration due to gravity on the planet will be?

Answer 1

Answer on Question #42596 – Physics - Mechanics | Kinematics | Dynamics

if a mass of a planet is 10% less than that of earth and the radius 20% greater than that of earth the acceleration due to gravity on the planet will be?

Solution:

$g_{e}$ – acceleration due to gravity of the Earth;

$g_{p}$ – acceleration due to gravity of the planet;

$M_{p} = 0.9M_{e}$ – mass of the planet;

$R_{p} = 1.2R_{e}$ – radius of the planet;

Formula for the acceleration due to gravity (gravitation equation):

$$g_{e} = G \frac{M_{e}}{R_{e}^{2}} \quad (1)$$ $$g_{p} = G \frac{M_{p}}{R_{p}^{2}} = G \frac{0.9 M_{e}}{(1.2 R_{e})^{2}} \quad (2)$$ $$(2) \div (1):$$ $$\frac{g_{p}}{g_{e}} = \frac{\frac{0.9 M_{e} G}{(1.2 R_{e})^{2}}}{\frac{M_{e} G}{R_{e}^{2}}} = \frac{0.9 M_{e} G}{(1.2 R_{e})^{2}} \cdot \frac{R_{e}^{2}}{M_{e} G} = \frac{0.9}{1.2^{2}}$$ $$g_{p} = g_{e} \frac{0.9}{1.2^{2}} = 0.625 \cdot 9.8 \frac{m}{s^{2}} = 6.13 \frac{m}{s^{2}}$$

Answer: acceleration due to gravity on the planet will be $6.13 \frac{m}{s^{2}}$.

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