Question

A boat floating in fresh water displaces $16000N$ of water how many Newton of salt water would it displace if it floats in saltwater of specific gravity $1.17$ ?
A) $14500N$
B) $17600N$
C) $16000N$
D) $28400N$

Answer 1

Hint:When a boat floats on water it displaces a weight of water equal to its own weight when a boat floats on water displaces a weight of fluid equal to its own weight. Every ship, submarine, and dirigible must be designed to displace a weight of fluid at least equal to its own weight.

Complete step by step answer:
When a boat place in water two forces acts on it one is weight of boat in downward direction and second is buoyant force applied by water in upward direction
A boat only can float when the weight of displaced water equals the weight of the boat the boat will sink until the buoyant force equals its weight. So the law of flotation states that a floating object displaces its own weight of the fluid in which it floats.
I.e. Weight of floating object= weight of fluid displaced.............. (1)
Or we can say that Mass of floating object = mass of fluid displaced
In this question we do not change the boat means the weight of the boat remains the same in all liquids whatever we use if the boat is floating that means it displaced the same amount of weight of water equal to its own weight.
So in salt water boat displaced same weight of water as displaced in other types of liquid because in both types of water boat is floating
So in this question from equation (1)
Weight of boat = weight of fresh water displaced......... (2)
When boat floats in salt water then
Weight of boat = weight of salt water displaced.......... (3)
Boat is same so weight of boat is same
(2)= (3)
Weight of boat = weight of fresh water = weight of salt water = $16000N$

Hence option C is correct

Note: Sometimes you may confuse why density does not affect the answer. Any changes in the density of the surrounding liquid affects the level in which an object floats. Means if density of water changes the part of the object inside the water is also changes if density increases then part of the boat sinks in water decreases. Thus, you have to remember that an object will displace the amount of water or liquid that is equal to its own mass in order to float.