Question

You drop a solid sphere of aluminium in a bucket of water that sits on the ground. The buoyant force equals the weight of water displaced; this is less than the weight of the sphere, so the sphere sinks to the bottom. If you take the bucket with you on an elevator that accelerates upward, the apparent weight of the water increases and the buoyant force on the sphere increases. Could the acceleration of the elevator be great enough to make the sphere pop up out of the water? Explain.

Short answer

No, the acceleration of the elevator will not be enough to make the sphere pop up out.

Step-by-step solution

Understanding the apparent weight

The apparent weight of any particular accelerating body is equivalent to the vector addition of body’s original weight and the negative of entire acceleration forces of the body.

Determining whether the sphere will pop out of the water or not

It is mentioned in the question that as the bucket of water is taken on an elevator accelerating upward, its apparent weight rises along with the buoyant force on the sphere. But the apparent weight of the sphere rises too, and there won’t be enough buoyant force on the elevator to exceed the weight of the sphere and displace it out of water.

Thus, the acceleration of elevator won’t be enough to bring the sphere out of the bucket.