Question

Известно, что ускорение свободного падения на некоторой планете такое же, как и на Земле, а радиус её в 4 раза меньше радиуса Земли. Определите отношение массы данной планеты к массе Земли.

Answer 1

mg=G*m*M/R²

g=G*Mз/Rз²

g=G*Mпл/(Rз/4)²=G*Mпл/(16*Rз²)

Ускорение не изменилось, а знаменатель уменьшился в 16 раз.

Значит масса в 16 раз больше.

Мпл/Мз=16.

Answer 2

Calculation of the Mass Ratio of the Planet to Earth

To determine the mass ratio of the given planet to Earth, we can use the concept of gravitational acceleration. The gravitational acceleration on a planet is given by the formula:

g = G * (M / R^2)

Where: - g is the gravitational acceleration - G is the gravitational constant - M is the mass of the planet - R is the radius of the planet

Given that the acceleration due to gravity on the given planet is the same as on Earth, and the radius of the planet is 4 times smaller than the radius of Earth, we can set up the following equation:

g_planet = g_earth

G * (M_planet / R_planet^2) = G * (M_earth / R_earth^2)

Since the gravitational constant G is the same for both planets, we can cancel it out:

(M_planet / R_planet^2) = (M_earth / R_earth^2)

Now, we can substitute the given information into the equation. Let's assume the mass of Earth is M_earth and the radius of Earth is R_earth. The mass of the given planet will be M_planet and the radius of the given planet will be R_planet.

Given: - g_planet = g_earth - R_planet = (1/4) * R_earth

Substituting the values into the equation:

(M_planet / (1/4 * R_earth)^2) = (M_earth / R_earth^2)

Simplifying the equation:

(M_planet / (1/16 * R_earth^2)) = (M_earth / R_earth^2)

Cross-multiplying:

M_planet = (1/16) * M_earth

Therefore, the mass of the given planet is 1/16 times the mass of Earth.

Answer:

The mass of the given planet is 1/16 times the mass of Earth.