Aboat displaces a volume v of water as it floats on a fresh-water lake. when the boat moves into the ocean, what volume of salt water will it displace? (the density of fresh water is 1.0 kg/l, and the density of salt water is 1.02 kg/l)
a) 1.02 v
b) 0.98 v
c) v (the same volume)
d) 1.04 v

Option (b)

Explanation:

let the weight of boat is W.  In equilibrium condition, the weight of boat is equal to the buoyant force acting on the boat.

The buoyant force acting on the boat is equal to the weight of water displaced by the boat.

In case of fresh water:

Weight of the boat = weight of fresh water displaced by the boat

W = Volume of fresh water displaced x density of fresh water x g

W = V x 1 x g

W = V x g (1)

In case of salt water:

Let the volume of salt water displaced is V'.

Weight of the boat = weight of salt water displaced by the boat

W = Volume of salt water displaced x density of salt water x g

W = V' x 1.02 x g     (2)

Equate equation (1) and equation (2), we get

V x g = V' x 1.02 x g

V' = 0.98 V

Thus, option (b) is true.