What would be the acceleration (m/s2) due to gravity on a planet whose mass is 1/7th the mass of the earth and radius half the radius of the earth (g = 9.8 m/s2)a.4.2b.5.6c.3.4d.4.9

To calculate the acceleration due to gravity on a planet, we can use the formula:

g = (G * M) / (R^2)

Where: g is the acceleration due to gravity, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), M is the mass of the planet, and R is the radius of the planet.

Given that the mass of the planet is 1/7th the mass of the Earth and the radius is half the radius of the Earth, we can substitute these values into the formula.

Let's denote the mass of the Earth as ME and the radius of the Earth as RE.

M = (1/7) * ME R = (1/2) * RE

Substituting these values into the formula, we get:

g = (G * (1/7) * ME) / ((1/2) * RE)^2

Simplifying further:

g = (2 * G * ME) / (49 * RE)

Now, we can substitute the value of the acceleration due to gravity on Earth (g = 9.8 m/s^2) and solve for the acceleration on the planet.

9.8 = (2 * G * ME) / (49 * RE)

Rearranging the equation to solve for g:

g = (9.8 * 49 * RE) / (2 * G * ME)

Now, we can substitute the known values for G and ME:

g = (9.8 * 49 * RE) / (2 * (6.67430 × 10^-11) * ME)

Calculating this expression will give us the acceleration due to gravity on the planet.