A small solid sphere of mass M0, of radius R0, and of uniform density 0 is place

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 = 0 and mass M < M0

2.The new sphere has radius R = R0 and mass M > M0

3. The new sphere has density = 0 and radius R > R0

4. The new sphere has density < 0 and radius R > R0

5.The new sphere has mass M = M0 and radius R > R0

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

Explanation / Answer

1. Bouyancy can be understood as an upward thrust (force) felt by an object when immersed in water. The objects floats till it displaces water = its mass. For example, 1 gm of object will displace 1 gm/cc water to float.

In the question the sphere is replacerd by another with M < Mo, thus, the water level will fall (F) below L.

2. When mass M > Mo, the water level rises (R) above L.

3. Bouyant force = * g * h (where is density of the object). When R > R0, the volume of the object increases. But = 0, to compensate this the mass of the object has to increase. And since, the density remains same the water level also remains same (U).

4. R > R0, that means volume increases and < 0 , that means density decreases and hence water level will fall below L (F).

5. The new sphere has mass M = M0 and radius R > R0, that is volume increase. Therefore, density decreases and water level will fall below L (F).

6. The new sphere has radius R < R0, that is volume decreases and mass M = M0. Therefore, density increases and hence the amount of water displaced will be more thus, giving a rise in the water level (R).

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.