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.

1. The new sphere has density p > p0 and radius R < R0
2.The new sphere has mass M = M0 and density > 0
3. The new sphere has radius R = R0 and density > 0
4. The new sphere has density < 0 and mass M = M0
5. The new sphere has density = 0 and mass M < M0
6. The new sphere has radius R > R0 and density = 0

Thanks!

Explanation / Answer

level of watre will increase by the volume of water displaced by sphere for buoyant force.

Fb = Vd x rho_water x g

and for equilibrium , buoyant force =weight force

V_displaced x rho_wwter x g = V_sphere x rho_sphere x g

V_displaced = V_sphere x rho_sphere /(rho_water) Or mass of sphere / rho_water

V_sphere = 4 pi R^3 / 3

V_displaced = constant ( R^3 x rho )

V_displaced is propotional to the water level;

1: rho increase but V_sphere ( propotional to radius) is decreases.

so relation between them needed by how much they increases to decreases.
without relation it may fall, rise or remain same.

(if they are increase or decrease with same amount then level Falls )

2. mass unchanged then V_displaced will also unchanged.

Level -> Unchanged

3. rho increaes then level increases

4. Mass unchanged so level unchanged

5. mass decreases so level falls.

6.R increases so level Rises/

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