a solid sphere of mass m and radius r is plced nside as hollow thin spherical shell of mass and M and radius R as shown in figure. A particle of mas m is placed on tehline joining the tow centres ast a distance x from the point of contct of th sphere and teh shell. Findn teh mgnitude fo the resultant gravitational force on this particle due to the sphere and the shell if a. `rltxlt2r, b. 2rltxlt2R and c. xgt2R`.

Answer

A, B, C

Explanation

a. `m_1` is placed at a distance x from O
If rltxlt2r`, Let's consider a thin shell of mass. ltbr. `dm=m/((4/3)pir^3)xx4/3pix^3=(mx^3)/r^3`
Thus `int dm=(mx^3)/r^3`
Then gravitatioN/Al force
`F=(Gmdm)/x^2`
`=(8(mx^3)/r^3)/x^2=(Gmx)/r^3`
`b `2rltxlt2R`, then F is due to only the sphere,
`:. F=(Gmm^1)/((x-r)^2)`
c. If xlt2R then gravitatioN/Al force is due to both sphere and shelll then
due to shell `F=(GMm^2)/((x-R)^2)`
Due to the sphere `=(gmm^1)/((x-r)^2)`
So, resultant force `e=(gmm^1)/((x-r)^2) +(GMm^1)/((x-R)^2)`