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.

R F U R or U F or U R or F or U  The new sphere has radius R = R0 and density < 0
R F U R or U F or U R or F or U  The new sphere has radius R > R0 and density = 0
R F U R or U F or U R or F or U  The new sphere has density = 0 and radius R < R0
R F U R or U F or U R or F or U  The new sphere has radius R < R0 and mass M = M0
R F U R or U F or U R or F or U  The new sphere has radius R > R0 and mass M = M0
R F U R or U F or U R or F or U  The new sphere has density < 0 and radius R > R0

Explanation / Answer

We know: submerged volume, Vsub = (o/w)Vo

where o = density of sphere, w = density of water, Vo = volume of sphere

a) density decreases, submerged volume decreases, so water level falls

b) radius increases, volume of sphere increases, submerged volume increases, so water level rises

c) radius decreases, volume of sphere decreases, submerged volume decreases, so water level falls

d) mass is same, the product oVo reamins same, so submerged volume remains same, so water level remains unchanged

e) same as part 'd'

f) cant be concluded since the quantity of change in both facotrs is needed.

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