A rock has mass 1.80 kg. When the rock is suspended from the lower end of a string and totally immersed in water, the tension in the string is 12.8 N. What is the smallest density of a liquid in which the rock will float?

3644.63 kg/m^3

Explanation:

mass of rock, m = 1.80 kg

Weight of rock in water = 12.8 N

Weight of rock in water = Weight of rock in air - Buoyant force on the rock due to water

Buoyant force in water = 1.8 x 9.8 - 12.8 = 17.64 - 12.8 = 4.84 N

Volume x density of water x g = 4.84

V x 1000 x 9.8 = 4.84

V = 4.939 x 10^-4 m^3

For the rock to float in a liquid

Buoyant force due to liquid on rock = weight of the rock

V x density of liquid x g = 1.80 x g

density of liquid = 1.80 / (4.939 x 10^-4) = 3644.63 kg/m^3