The diameter and mean density of jupiter are 11 times and times respectively to that of Earth.If the gravitational intensity at the surface of Earth is 10 N kg-1 what is the gravitational intensity atthe surface of jupiter?
Question
The diameter and mean density of jupiter are 11 times and times respectively to that of Earth.If the gravitational intensity at the surface of Earth is 10 N kg-1 what is the gravitational intensity atthe surface of jupiter?
Solution
The formula for gravitational intensity (g) is given by:
g = GM/r^2
where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.
Given that the diameter and mean density of Jupiter are 11 times and 1 times that of Earth respectively, we can say that the radius of Jupiter is also 11 times that of Earth.
The mass of a planet is given by its volume (which is proportional to the cube of the radius) times its density. Therefore, the mass of Jupiter is 11^3 = 1331 times that of Earth.
Substituting these values into the formula for g, we get:
g_Jupiter = G * (1331 * M_Earth) / (11 * r_Earth)^2
Simplifying this, we get:
g_Jupiter = G * M_Earth / r_Earth^2 * (1331 / 11^2)
Since G * M_Earth / r_Earth^2 is the gravitational intensity at the surface of Earth (which is given as 10 N kg^-1), we can substitute this value in to get:
g_Jupiter = 10 * (1331 / 11^2)
Solving this, we get:
g_Jupiter = 10 * (1331 / 121) = 110 N kg^-1
Therefore, the gravitational intensity at the surface of Jupiter is 110 N kg^-1.
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