Question

a solid sphere is an equilibrium in water in such a way that its three fourth volume inside the water calculate the density of material of sphere in kg​

Answer 1

The density of the sphere is 750kg/m^3

-The given problem can be analysed using condition of static equilibrium ( A body is said to be in static equilibrium if the net force and torque acting on the body is zero)

-Here we don't have any Torque as the body is not rotating.

-The two forces we have are the weight of the body and buoyant force which are acting opposite to each other.

Let density of sphere is D

     density of water d=1000 Kg/m^3

     volume of sphere is V

     acceleration due to gravity is g

     mass of the sphere is M

-Weight of the body = M.g

                                  =D.V.g

-buoyant force = d.V(inside water).g

we have V(inside water)=0.75V  (given)

-equating the forces, we have

D.V.g = d.V(inside water).g

D.V.g = d.(0.75V).g

D = 0.75d

D=0.75*1000=750 Kg/m^3