Question

The radius of the moon is 27% of the earth's radius and it's mass is 1.2% of the earth's mass. Find the the acceleration due to gravity on the surface of the moon.



Answer is 1.615 m/s*2
But how ??
Explain it .

Answer 1

The acceleration due to gravity on the moon is 1.615 m/s^2

The force applied by an object on the planet, F=mg

and the force applied by planet on the object due to gravity, F=$\frac{GMm}{r^{2} }$

On comparing both the forces

The force of gravity on the planet is given as

g=$\frac{GM}{r^{2} }$

Now the gravity of the moon is calcualted as

\frac{g_m}{g_e}=\frac{(GM_m)/(r_m)^2}{(GM_e)/(r_e)^2}

Plugging the values

\frac{g_m}{9.8}=\frac{(0.012M_e)/(0.27r_e)^2}{(GM_e)/(r_e)^2}

(g_m)/9.8=0.012/0.0729

g_m=1.615 m/s^2

Answer 2

The acceleration due to gravity on the moon is 1.615 m/s^2

The force applied by an object on the planet, F=mg

and the force applied by planet on the object due to gravity, F=\frac{GMm}{r^{2} }

r

2

GMm

On comparing both the forces

The force of gravity on the planet is given as

g=\frac{GM}{r^{2} }

r

2

GM

Now the gravity of the moon is calcualted as

\frac{g_m}{g_e}=\frac{(GM_m)/(r_m)^2}{(GM_e)/(r_e)^2}

Plugging the values

\frac{g_m}{9.8}=\frac{(0.012M_e)/(0.27r_e)^2}{(GM_e)/(r_e)^2}

(g_m)/9.8=0.012/0.0729

g_m=1.615 m/s^

I think this is the only way to do it