physics

posted by .

spherical aluminum ball of mass 1.22 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water.Calculate the radius of the cavity.

• physics -

r = inner radius (of spherical cavity)

Sphere weight = buoyancy force

(4/3) pi (R^3 - r^3)*(density of Al)*g
= (4/3) pi R^3 * (density of water)*g

(4/3) pi R^3 * (density of water)
= 1.22 kg

(Use the second equation to solve for R)

The (4/3) pi g cancels out in the first equation.

1 - (r/R)^3
= (water density)/(Al density)

Look up the densities and solve

Similar Questions

1. physics

An irregularly shaped chunk of concrete has a hollow spherical cavity inside. The mass of the chunk is 32kg, and the volume enclosed by the outside surface of the chunk is 0.020m^3. What is the radius of the spherical cavity?
2. Physics

Consider a conducting spherical shell with inner radius b = 0.862 m and outer radius c = 1.21 m. There is a net charge q2 = 3.82 ìC on the shell. At its center, within the hollow cavity, there is a point charge q1 = 2.89 ìC. Determine …
3. PHYSICS!!!! help!!!

A perfectly spherical, but squishable ball of radius 10 cm is blown up to an internal pressure of 2 atm. The ball is placed between two perfectly vertical walls and the walls are slowly squeezed together. Initially the ball slips down …
4. Physics

If the spherical ball is negatively charged.How the mass of the sphere or ball get effected?
5. math

a 150g-iron ball at 95 Celsius is dropped into a cavity in a block of ice.the cavity is then found to contain 21 g of water . calculate the heat of fusion of ice.
6. math

a 150g-iron ball at 95 Celsius is dropped into a cavity in a block of ice.the cavity is then found to contain 21 g of water . CALCULATE THE HEAT OF FUSION OF ICE (The specific heat capacity of iron is 0.11 cal/g x C degrees.)
7. physics/chemistry

how does one calculate the work done by a spherical bubble with radius r in a liquid with a surface tension of T. I understand for a cavity it is 8pi(r)T, would you just double it to get 16pi(r)T because there are 2 films?
8. physics

A 150g iron ball is dropped into a cavity in a block of ice. The cavity is then found to contain 21g of water. Calculate the heat of fusion of ice.
9. algebra

Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of centimeters. What is the volume of air in the spherical ball?
10. Chemistry 101

A spherical ball has a diameter of 1.00 inch and a mass of 2.00grams. Will the ball float or sink in water?

More Similar Questions