Saved Bookmarks
| 1. |
On to a sphere of radius R//2 and density P_(2) with centre at C_(2) a second solid sphere is moulded with density p_(1) radius R and centre C_(1). Find the force experienced by a point mass m at point P at a distance y from the combination as shown. |
|
Answer» Solution :If we consider that a sphere of RADIUS `R` is PLACED with centre at `C_(1)` od density `rho_(1)` the force on the mass at `P` is `F_(1)=G((4//3)piR^(3)rho_(1)m)/((R+y)^(2))` towards the sphere. If we consider that a sphere of radius `R//2` is placed with centre at `C_(2)` of density `rho_(1)` the force on the mass at `P` is `F_(2)=G((4//3)pi(R//2)^(3)rho_(1)m)/((R//2+R+y)^(2))` towards the sphere. If we consider that a sphere of radius `R//2` is placed with centre at `C_(2)` of density `rho_(2)` the force on the mass in at `P` `F_(3)=(G(4//3)pi(R//2)^(3)rho_(2)m)/((R//2+R+y)^(2))` By the PRINCIPLE of superposition `F=F_(1)-F_(2)+F_(3)=(4)/(3)piR^(3)Gm[(rho_(1))/((R+y)^(2))+((rho_(2)-rho_(1))//8)/(((3R//2)+y)^(2))]` |
|