Question

A man sits in a boat, which is floating on the surface of a pond. He takes a rock from inside of the boat and throws it overboard into the pond, determine whether the level of the pond would rise, fall or remain unchanged? Support your answer with calculations

Answer 1

Let us assume mass of man =

Mass of the rock =

Mass of Boat =

According to archimedis defination on buoyancy force, that the buoyancy force is equals to the weight of the body acted on it or amount of fluid displaced.

Therefore

Where Initial volume of fluid displaced.

Now the rock was thrown into the pond than the new buoyancy force will be

Where Final volume of fluid displaced after rock thrown

Now we may conclude that   

Substute equations (1) and (2) in above, we get

And we know that

Similarly calculate the initial displaced volume   

Now

  

Since density of rock is more than the density of water. It concludes that,

     

Therefore the water level in the pond decreases from the initial level