The gravitational force on a small mass m located at the center of a spherical cavity within a planet can be calculated using the principles of gravitational attraction and the properties of spherical shells. The correct formula for the gravitational force is F = (2/3)Gπdm, where d is the density of the planet and G is the gravitational constant. The initial incorrect calculation of 16Gπdm/3 was clarified through the understanding of the gravitational effects of the surrounding mass and the concept of treating the cavity as filled with negative mass. This approach simplifies the calculation by considering the net effect of the surrounding material.
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As per forum rules, you should quote any relevant standard equations of which you are aware and must show some attempt at a solution. If totally stuck, you should at least be able to provide some thoughts.anshuman3105 said:A large spherical planet of radius R made of a material of density d, has a spherical cavity of radius R/2, with center of cavity a distance R/2 from the centre of the planet. Find the gravitational Force on a small mass m at the centre of the cavity
I get ##\frac 23 G\pi d r m## (I'm guessing the "/2" in what you posted is a typo).anshuman3105 said:using the formula F = Gm1m2/r^2, i am getting 16Gpidrm/3 but the solution is 2Gpidrm/2
That formula is essentially for point masses. It also works if one mass is a uniform spherical shell (or assembly of concentric uniform spherical shells) and the other (point) mass is outside all the shells.anshuman3105 said:I used Gm1m2/r^2
http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshell2.htmlanshuman3105 said:Can you show it to me the solved part..?