If a planet has a radius 20% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?Select one:a.6.8 m/s2b.14 m/s2c.12 m/s2d.8.2 m/s2
Question
If a planet has a radius 20% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?Select one:a.6.8 m/s2b.14 m/s2c.12 m/s2d.8.2 m/s2
Solution
The acceleration due to gravity on the surface of a planet is given by the formula:
g = GM/r^2
where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.
In this case, the mass of the planet is the same as the Earth's, so M is the same for both. However, the radius of the planet is 20% greater than the Earth's. This means that r for the planet is 1.2 times the Earth's radius.
The acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s^2. So we can write the equation for the Earth as:
9.8 = GM/(r_earth)^2
and for the planet as:
g_planet = GM/(1.2*r_earth)^2
Dividing the second equation by the first to eliminate GM gives:
g_planet/9.8 = (r_earth/1.2*r_earth)^2
Solving for g_planet gives:
g_planet = 9.8 * (1/1.2)^2
g_planet = 9.8 * (0.833)^2
g_planet = 9.8 * 0.694
g_planet = 6.8 m/s^2
So, the acceleration due to gravity at the surface of the planet is approximately 6.8 m/s^2. The correct answer is a. 6.8 m/s^2.
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