A solid sphere of radius R gavitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity radius is made in the sphere (as shown in the image) and the force becomes F2. The value F1 :F2 is:
Option: 1 41 :50
Option: 2 36:25
Option: 3 50:41
Option: 4 25 :36
Let the initial mass of the sphere is M.
If a spherical part of radius is taken out from the big sphere, then the mass of the remaining sphere is
Hence mass of removed portion will be
From the figure it is clear that
From superposition principle,
Here force due to remaining part
force due to mass on the cavity
As
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