A small solid sphere of Mass M0, of radius R0, and of uniform density p0 is plac

Question

A small solid sphere of Mass M0, of radius R0, and of uniform density p0 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 density = 0 and radius R > R0

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

R, F, U, R or U, F or U, R or F or U The new sphere has mass M < M0 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 mass M = M0 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

Please select R, F, U, R or U, F or U, R or F or U for each question. Thanks for the help!

Explanation / Answer

here,

the level of water in the dish,

depends on the mass of the solid sphere

(A)

when p = p0 nd R > R0

the volume is incresed and mass also increses,

then the water level Rises

(B)

when M = M0 and p < p0

the level is unchanged

(C)

when M<M0 and p = p0

the mass is decreased,

so, the level falls

(D)

when R = R0 and p < p0

mass = density * volume

the mass also decreases,

and the level decreases

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