Assuming the earth to be a uniform sphere of radius 6400 km and density 5.5g/c.c. find the value of g on the surface where G=6.67×10
F = m g = G M m/r^2
actually G = 6.67 * 10^-11
r = 6,400,000 meters = 6.4 * 10^6
rho = 5.5 *10^3 Kg/m^3
M = rho*(4/3) pi r^3 = 23*10^3 r^3
m g = m *6.67*10^-11 *23*10^3 r^3/r^2
g = 6.67*23 *10^-8 (6.4*10^6)
= 983 *10^-2
= 9.83 m/s^2
close enough :)
if the radius of Earth had been listed as 6378km, it would have been very close.
To find the value of "g" on the surface of the Earth, you need to use the formula for gravitational acceleration:
g = (GM) / r^2
where:
g is the gravitational acceleration
G is the gravitational constant, which is approximately 6.67 x 10^(-11) Nm^2/kg^2
M is the mass of the Earth
r is the radius of the Earth
First, we need to find the mass of the Earth. The volume of a sphere can be calculated using the formula:
V = (4/3) π r^3
where:
V is the volume
π is a constant (approximately 3.14159)
r is the radius of the sphere
Since the density of the Earth is given as 5.5g/cc, this means that every cubic centimeter of the Earth weighs 5.5 grams. Therefore, the mass can be calculated as:
M = V * density
Substituting the value of "density" as 5.5 g/cc and rearranging the previous equation, we get:
M = (4/3) π r^3 * density
Now, let's calculate it step by step:
Step 1: Calculate the volume of the Earth using the given radius.
V = (4/3) * π * (6400 km)^3
Step 2: Convert the volume from cubic kilometers to cubic centimeters.
V = (4/3) * π * (6400 km)^3 * (1 km/100000 cm)^3
Step 3: Multiply the volume by the density to find the mass of the Earth.
M = V * density
Step 4: Substitute the values into the formula for gravitational acceleration.
g = (G * M) / r^2
Step 5: Convert the radius from kilometers to centimeters.
r = 6400 km * 100000 cm/km
Substituting all the values into the formula for gravitational acceleration, you can calculate the value of "g" on the surface of the Earth.