Question

A boat with an anchor on board floats in a swimming pool that is somewhat wider than the boat. Does the pool water level move up, move down, or remain the same if the anchor is (a) dropped into the water or (b) thrown onto the surrounding ground? (c) Does the water level in the pool move upward, move downward, or remain the same if instead; a cork is dropped from the boat into the water, where it floats?

Short answer

(a) The level of the pool water moves downward if the anchor is dropped into the water.

(b) The level of the pool water moves downward if the anchor is thrown onto the surrounding ground.

(c) The water level in the pool remains same if instead, a cork is dropped from the boat into the water, where it floats.

Step-by-step solution

The given data 

Conditions for the total weight of the boat are given.

Understanding the concept of the Archimedes Principle

The water level increases according to the weight of the object submerged in it. Thus, using the given data and situations, we can get the weight of the object.

Formula:

The weight on a body due to gravitational acceleration, W = mg (i)

Calculation of the water level when anchor is dropped into the water

a)

If the anchor is dropped down into the water, the weightof the boatreduces due to decrease in the weight of the boat considering equation (i). So, it displaces less water than before.

Hence, the level of water moves downward.

Calculation of the water level when anchor is thrown into the surrounding ground

b)

If the anchor is thrown onto the surrounding ground, the level of water moves downward because the boat will displace less water than before.

Hence, the level of water moves downward.

Calculation of the water level when cork is dropped into the river where it floats

c)

When cork is droppedfrom a boatinto the water, then there would be no effect on the weight of the boat. So, it displaces the same volume of water as before.

Hence, there would be no effect on the level of water.