Question

A fisherman and his young daughter are in a boat on a small pond. Both are wearing life jackets. The daughter is holding a large floating helium filled balloon by a string. Consider each action below independently, and indicate whether the level of the water in the pond R-Rises, F-Falls, S-Stays the Same, C-Can't tell. (If in the first the level Rises, and in the second it Falls, and for the rest one Cannot tell, enter RFCCC)

A) The fisherman lowers himself in the water and floats on his back
B) The fisherman knocks the tackle box overboard and it sinks to the bottom.
C) The daughter pops the balloon.
D) The fisherman fills a glass with water from the pond and drinks it.
E) The daughter gets in the water, looses her grip on the string, letting the balloon escape upwards.

Answer 1

Ans:-

As we know,

1) The amount of water displaced by a floating object is equal to the object's weight. The amount of water displaced by a sinking object is equal to the object's size.

2) An object with a density less than water floats and thus displaces an amount of water equal to its weight.

3) An object with a density greater than water sinks and thus displaces an amount of water equal to its volume (which is less than the amount of water equal to its weight).

4) More displacement means the level of the pond rises. Less displacement means the level falls.

A) Stays the same. He is floating in both cases so the amount of water displaced is determined by his weight in both cases.

B) Falls. Since the box sinks, the amount of water displaced by the box when it is in the boat is more than the volume of the box.

C)  Rises. The weight increases and the boat presumably continues to float, so the displacement increases. If it is possible that the boat would sink after the balloon pops, then the answer is Can't tell.

D) Stays the same. The increased displacement due to the weight of the water being drunk is the same as the volume of the water removed from the pond.

E)  Rises. Assuming he floats (we don't want him to drown), then the weight increases so the displacement increases.