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.

******Options for the follwowing question are R,F,U, R or U, F or U, and F or R or U

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

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

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

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

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

The new sphere has radius R > R0 and mass M = M0

Explanation / Answer

solid sphere comes in equilibrium when it has displaced the water pf same weight as itself.

m = (4 pi R0^3 / 3 )(rho0)

R is decreased and rho is increases.

so it may rise, fall or unchanged

F or R or U

R < R0 and rho = rho0
radius is decreases so mass.

hence level Falls

Ans F

rho = rho0 and M > M0

mass is increases hence leveel rises.

And R

rho > rho0 and M = M0

mass is same hence leveel remains unchanged.

Ans. U

R = R0 and rho < rho0

mass decreases.

Anss F

M = M0

mass is unchanged.

hence U.

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