A small solid sphere of mass M 0 , of radius R 0 , and of uniform density 0 is p

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.
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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

water level raised just because of the submerged volume of the floating sphere

rho 0 * Volme(sphere) * g =M0* g = balanced by bouncy force = rho(water) * Volume(submerged) * g

Volume(submerged) = rho 0 * volume(sphere) / rho(water) = M0 / rho(water)

1)

volume is same (R=R0) but rho < rho 0

Volume(submerged) is decreases so water level also decreases

2)

volume increases so Volume(submerged) is also increase and hence water lavel increases

3)

volume decreases so Volume(submerged) is also decrease and hence water lavel decreases

4)

mass is same so there is no change in submurged volume hence no change in water level

5)

same as 4

6)

we can not say about the submurged volume because hoe rho0 and R0 changed not given

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