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.

1) the new sphere has radius r > ro and mass m = mo

2)the new sphere has mass m < mo and density p=po

3)the new sphere has radius r > ro and density p = po

4) the new sphere has a mass m = mo and density p < po

5) the new sphere has density p > po and radius r < ro

6) the new sphere has radius r = ro and density p < po.

Explanation / Answer

The factors are: Pi = 3.141592654, r = radius, m = mass, d = density

m = (4/3)*d*Pi*r^3
[mass increases if <the density increases> or <the radius increases> or <both> or <the density increase exceeds the increase of the cube of the radius>] {Line 1: L or U} {Line 4: L}
[mass decreases if <the density decreases> or <the radius decreases> or <both> or <the increase of the cube of the radius exceeds the density increase>] {Line 4: L}
[mass does not change if <the density remains inversely proportional to the cube of the radius] {Line 4: U}

d = m/((4/3)*Pi*r^3)
[density increases if <the mass increases> or <the radius decreases> or <the both> or <the mass increase exceeds the decrease of the cube of the radius>] {Line 2: U}
[density decreases if <the mass decreases> or <the radius increases> or <the both> or <the mass decrease exceeds the increase of the cube of the radius>] {Line 5: L} {Line 6: U}

r = ((3*m)/(4*d*Pi))^-3
[radius decreases if mass decreases or density increases or both] {Line 3: L}

Displacement of water will cease when the density of the sphere becomes greater than the density of water. {Line 2: L}

1. L or U
2: R
3: U
4: L
5: L or R or U
6: L

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