A small solid sphere of mass M0, of radius R0, and of uniform density 0 is place

Question

A small solid sphere of mass M0, of radius R0, and of uniform density 0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

The new sphere has density > 0 and radius R < R0

The new sphere has density > 0 and mass M = M0

The new sphere has density < 0 and mass M = M0

The new sphere has density = 0 and mass M < M0

The new sphere has density = 0 and radius R > R0

The new sphere has radius R = R0 and density < 0

Explanation / Answer

The water level in the bowl is dependent on the amount of water displaced by the floating bodies. And the volume of the water displaced is dependent on the density and the weight (mg) of the floating body. If the density of the floating body decreses then the water displaced mainly depend on the weight of the floating body.

mass =volume X density

i)density more ,and radius is less so mass is more i.e water level increases (R)

ii)density more ,mass unchanged so volume decreases i.e water level unchanged (U)

iii)density decreases and mass unchanged so volume increses i.e water level unchnged (U)

iv)density unchanged and mass decresed so water level also decreases (F)

v)density unchanged and the radius increased so mass also increased i.e water level increased(R)

vi)radius is unchanged and the density is decresed then the mass also decresed so water level decreased (F)

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