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.
Options are Rises, Falls, Unchanged, R or U, F or U, and R or F or U. SERIOUS TUTORS PLEASE

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

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

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 radius R > R0

Explanation / Answer

From the buoyancy, we know that the a floating object displaces an amount of water of the same mass.

A.If mass is decreased =density decreases =then the level falls (F)

B.If the size is decreased then mass also decreases, threfore the level falls(F)

C.If the density increased but size is decreased, then there will be no change in mass(U)

D.If desnity is unchanged, then level is also unchanged(U)

E.If the mass is unchanged, level is unchaged (U)

F.If the size is increased, then mass also increases (R)

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