Question

Известно,что на некоторой планете ускорение свободного падения на 50% меньше,чем на Земле.На сколько процентов должна отличаться масса тела,находящегося на этой планете, от массы тела, находящегося на Земле, для того, что бы их силы тяжести были одинаковыми

Answer 1

Сила тяжести на Земле
F = m*g                                                                    (1)

Сила тяжести на планете
F₁ = m₁*g₁ = m₁*(0.5*g) = m₁*g / 2                         (2)

Приравняем (1) и (2)     -   они равны по условию задачи
m*g = m₁*g / 2    
m₁ = 2*m 

Масса должна быть в 2 раза больше (или на 100%)

Answer 2

Calculation of the Difference in Mass

To determine the percentage by which the mass of an object on a planet should differ from the mass of an object on Earth in order for their gravitational forces to be equal, we can use the concept of gravitational acceleration.

The acceleration due to gravity on Earth is approximately 9.8 m/s^2 Let's denote this value as g_E.

On the other planet, the acceleration due to gravity is 50% less than on Earth. Therefore, the acceleration due to gravity on the other planet can be calculated as:

g_other_planet = 0.5 * g_E

To find the mass difference required for the gravitational forces to be equal, we can use the formula for gravitational force:

F = m * g

where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity.

Since we want the gravitational forces to be equal, we can set up the following equation:

m_E * g_E = m_other_planet * g_other_planet

where m_E is the mass of the object on Earth, and m_other_planet is the mass of the object on the other planet.

Substituting the values of g_E and g_other_planet, we get:

m_E * 9.8 = m_other_planet * (0.5 * 9.8)

Simplifying the equation:

m_E = m_other_planet * 0.5

To find the percentage difference in mass, we can calculate:

percentage_difference = ((m_other_planet - m_E) / m_E) * 100

Let's calculate the percentage difference:

m_E = m_other_planet * 0.5

percentage_difference = ((m_other_planet - m_E) / m_E) * 100

Calculation:

m_E = m_other_planet * 0.5

percentage_difference = ((m_other_planet - m_E) / m_E) * 100

Now, we need to solve these equations to find the value of the percentage difference.