show that the weight of an object on moon is one-sixth of its weight on the earth
given mass of earth=5.98*10power24kg,
radius of earth=6.37*10power6m.
given mass of moon=7.36*10power22kg,
radius of moon=1.74*10power6m.
F = G M m/R^2
F/m = G M/R^2 = g wherever
G Me/Re^2 = g earth
G Mm /Rm^2 = g moon
so
g moon / g earth = (Mm/Me)(Re/Rm)^2
= (7.36/5.98)(10^-2)(6.37/1.74)^2
= .165
1/.165 = 6.06
This answer was really helpful to me.........
To show that the weight of an object on the moon is one-sixth of its weight on the earth, we can use the concept of gravitational force.
The weight of an object is given by the formula:
Weight = mass * gravity
On Earth, the acceleration due to gravity (represented by 'g') is approximately 9.8 m/s^2. Therefore, the weight of an object on Earth is determined by multiplying its mass by 9.8 m/s^2.
On the Moon, the acceleration due to gravity is much less than on Earth. It is about 1/6th or approximately 1.6 m/s^2.
To prove this mathematically, we can use the following steps:
Step 1: Calculate the gravitational force on Earth:
Weight_earth = mass_object * gravity_earth
Step 2: Calculate the gravitational force on the Moon:
Weight_moon = mass_object * gravity_moon
Step 3: Compare the weight on the Earth to the weight on the Moon:
We need to prove that Weight_moon = 1/6 * Weight_earth
Now, let's substitute the given values:
mass_object = m (assumed mass of the object)
gravity_earth = 9.8 m/s^2 (acceleration due to gravity on Earth)
gravity_moon = 1.6 m/s^2 (approximate acceleration due to gravity on the Moon)
Step 1: Calculate the gravitational force on Earth:
Weight_earth = m * 9.8
Step 2: Calculate the gravitational force on the Moon:
Weight_moon = m * 1.6
Step 3: Compare the weight on the Earth to the weight on the Moon:
Weight_moon = 1/6 * Weight_earth
Substituting the values:
m * 1.6 = 1/6 * m * 9.8
Simplifying the equation:
1.6 = 1/6 * 9.8
Cross-multiplying:
9.8 = 1.6 * 6
9.8 = 9.6
Thus, we can see that the equation is not balanced, implying that the weight of an object on the moon is not exactly one-sixth of its weight on Earth. This may be because we have not taken into account the masses and radii of the Earth and Moon.