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

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.

The new sphere has density -Po and radius R > R0 The new sphere has density R0 The new sphere has mass M Mo and radius RRo The new sphere has density -Po and radius R

Explanation / Answer

1. R

The density of the new sphere is same as the old shpere, hence it will also float, but it will displace more volume of the water because of higher radius and hence more mass. Therefore, the level of the water will rise.

2. F

The density of the new sphere is lesser than that of the old shpere, hence it will also float, but it will displace a lower volume of the water, since it has a lower mass than the old sphere. Hence, the level of the water will fall.

3. R

The mass of the new sphere is the same as that of the old shpere but it has a lower radius and so, more volume of water will be displaced. Hence, the level of the water will rise.

4. F

The ball has the same density, but lower radius. This means that the ball has lesser mass, and hence the level of the water will fall.

5. F

The new sphere has a lower density and it will hence float more than the old sphere, due to which less water will be displaced and the water level will fall.

6. F

The mass of the new sphere is the same but theradius is higher, which means that the density of the new sphere is low and it will float more than the old sphere. Hence, the level of the water will fall.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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