'the mass of the Earth is approximately 80 times the mass of the moon and the earth's radius 3.7 times that of the moon. if the acceleration of free fall on the Earth is 10 ms2. estimate its value on the moon'
g = 10(3.72^2)/80 = 1.73 m/sec.^2.
To estimate the acceleration of free fall on the moon, we can use the concept of gravitational acceleration. The acceleration due to gravity is given by the formula:
a = (G * M) / r^2
Where:
a = acceleration due to gravity
G = gravitational constant (approximately 6.67430 × 10^-11 m^3/kg/s^2)
M = mass of the celestial object
r = radius of the celestial object
Given that the mass of the Earth is approximately 80 times the mass of the moon and the Earth's radius is 3.7 times that of the moon, we can calculate the acceleration of free fall on the moon as follows:
1. Let's assume the mass of the moon as Mm and the radius of the moon as rm.
2. The mass of the Earth (Me) is approximately 80 times the mass of the moon: Me = 80 * Mm.
3. The radius of the Earth (re) is 3.7 times that of the moon: re = 3.7 * rm.
4. The acceleration due to gravity on the Earth (ae) is given as 10 m/s^2.
5. The acceleration due to gravity on the moon (am) can be calculated as am = (G * Mm) / rm^2.
Substituting the values and rearranging the formula, we can solve for am:
am = (ae * rm^2) / (re^2)
Let's calculate the value:
am = (10 * rm^2) / (3.7 * rm)^2
Simplifying further:
am = (10 * rm^2) / (13.69 * rm^2)
am = 0.7306 m/s^2
Therefore, the estimated value of the acceleration of free fall on the moon is approximately 0.7306 m/s^2.
To estimate the acceleration of free fall on the moon, we can use the concept of gravity. The acceleration of free fall is directly proportional to the gravitational force.
First, we know that the mass of the Earth is approximately 80 times the mass of the moon. Let's represent the mass of the Earth as Me and the mass of the moon as Mm.
Me = 80 * Mm
Next, we know that the Earth's radius is 3.7 times that of the moon. Let's represent the Earth's radius as Re and the moon's radius as Rm.
Re = 3.7 * Rm
The formula to compute the acceleration due to gravity is:
g = G * (Me / Re^2)
Where:
- g is the acceleration of free fall
- G is the gravitational constant (approximately 6.67430 * 10^-11 m^3⋅kg^-1⋅s^-2)
Substituting the known values, we have:
g (Earth) = 10 m/s^2
Me = 80 * Mm
Re = 3.7 * Rm
To estimate the value of g on the moon, we need to determine the ratio of the acceleration of free fall on the moon (g(moon)) to the acceleration of free fall on Earth(g(Earth)).
We can set up the following equation:
g(Earth) / g(moon) = (G * Me / Re^2) / (G * Mm / Rm^2)
Since G is the gravitational constant, it cancels out.
g(Earth) / g(moon) = (Me / Re^2) / (Mm / Rm^2)
Substituting the values we know:
10 m/s^2 / g(moon) = (80 * Mm / (3.7 * Rm)^2) / (Mm / Rm^2)
Now, we can simplify the equation:
10 m/s^2 / g(moon) = (80 * Rm^2) / (3.7 * Rm)^2
By rearranging the equation to solve for g(moon), we have:
g(moon) = 10 m/s^2 / ((80 * Rm^2) / (3.7 * Rm)^2)
Simplifying further gives:
g(moon) = 10 m/s^2 * (3.7 * Rm)^2 / (80 * Rm^2)
g(moon) ≈ 1.61 m/s^2
Therefore, the estimated acceleration of free fall on the moon is approximately 1.61 m/s^2.