Answer:
[tex]g_n=\dfrac{2}{9}g[/tex]
Explanation:
M = Mass of Earth
G = Gravitational constant
R = Radius of Earth
The acceleration due to gravity on Earth is
[tex]g=\dfrac{GM}{R^2}[/tex]
On new planet
[tex]g_n=\dfrac{G2M}{(3R)^2}\\\Rightarrow g_n=\dfrac{2GM}{9R^2}[/tex]
Dividing the two equations we get
[tex]\dfrac{g_n}{g}=\dfrac{\dfrac{2GM}{9R^2}}{\dfrac{GM}{R^2}}\\\Rightarrow \dfrac{g_n}{g}=\dfrac{2}{9}\\\Rightarrow g_n=\dfrac{2}{9}g[/tex]
The acceleration due to gravity on the other planet is [tex]g_n=\dfrac{2}{9}g[/tex]
Answer:
2 g/9
Explanation:
mass of planet, Mp = 2 x Me
radius of planet, Rp = 3 x Re
Where, Me is the mass of earth and Re is the radius of earth.
The formula for acceleration due to gravity on earth is given by
[tex]g = \frac{GM_{e}}{R_{e}^{2}}[/tex] .... (1)
The acceleration due to gravity on the planet is given by
[tex]g' = \frac{GM_{p}}{R_{p}^{2}}[/tex]
By substituting the values, we get
[tex]g' = \frac{2GM_{e}}{9R_{e}^{2}}[/tex] ..... (2)
Divide equation (2) by equation (1), we get
g'/g = 2/9
g' = 2 g/9
Thus, the acceleration due to gravity on th enew planet is 2 g/9.
