Calculate the mass of moon if free fall acceleration near it surface is know be 1.62 m/s^2 ( radius of moon is 1738 Km )
Mm= mass of moon
gm = acceleration of a free falling body on moon
G= universal gravitational constant
Since g = G× Mm/ Rm²
Ie.Mm= g× Rm²/G
m a = G m Mmoon /R^2
so
1.62 = G Mmoon/(1.738*10^6)^2
Good
To calculate the mass of the moon, we can use the formula for gravitational acceleration:
g = (G * M) / R^2
where,
g is the free-fall acceleration near the surface of the moon (given as 1.62 m/s^2),
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 / (kg * s^2)),
M is the mass of the moon (what we need to calculate),
R is the radius of the moon (given as 1738 km, we need to convert it to meters by multiplying by 1000).
Rearranging the formula, we have:
M = (g * R^2) / G
Substituting the known values into the formula:
M = (1.62 m/s^2 * (1738 km * 1000)^2) / (6.67430 x 10^-11 m^3 / (kg * s^2))
To simplify the calculation, we convert the units before performing the calculations:
M = (1.62 m/s^2 * (1738 * 1000)^2) / (6.67430 x 10^-11)
Now we can perform the calculation:
M ≈ 7.352 x 10^22 kg
Therefore, the mass of the moon is approximately 7.352 x 10^22 kilograms.