In: Physics
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 12.6 N .
What is the smallest density of a liquid in which the rock will float?
Express your answer with the appropriate units.
Mass of rock m = 1.8 kg
Weight of rock in water W = mg
= 1.8 x9.8
= 17.64 N
Tension in the string T = 12.6 N
So, loss of weight in water = F - T
= 17.64 N - 12.6 N
= 5.04 N
Specific gravity of a rock = weight of the rock in air / loss of weight in water
= 17.64 N / 5.04 N
= 3.5
Density of rock = Specific gravity of rock x density of water at 4 o C
= 3.5 x 1000 kg/ m3
= 3500 kg/ m3
If the rock is floats in liquid,the density of the liquid is greaterthan equal to density of rock.
Therefore the smallest density of a liquid in which the rock will float = 3500 kg/ m3