Answer:
free-fall acceleration = 12.25 m/s²
Explanation:
Formula for free fall acceleration is given by the gravity equation;
g = Gm/r²
Where;
M is mass of the Earth
r is radius of the Earth
G is the gravitational constant
Now, that equation applies to the earth.
For this new planet, we are told that the mass = 5 × mass of earth
And radius = 2 × radius of earth.
Thus, free fall acceleration for this planet is;
g_p = G(5m)/(2r)²
g_p = (5/4)(Gm/r²)
Gravitational constant has a value of 6.674 × 10^(−11) N.m²/kg²
Mass of the earth = 5.972 × 10^(24) kg
Radius of the earth = 6378 km = 6378000
Thus;
g_p = (5/4)(6.674 × 10^(−11) × 5.972 × 10^(24))/(6378000²) = 12.25 m/s²
