Question

A body of volume V and density ρ is kept completely immersed in a liquid of density ρ_L . If g is the acceleration due to gravity, write expressions for the following — (a) The weight of the body, (b) The upthrust on the body, (c) The apparent weight of the body in liquid, (d) The loss in weight of the body.

March 17, 2024

Answer

Given,

volume = V

density = ρ

density of liquid = ρ_L

acceleration due to gravity = g

(i) The weight of the body, acting downwards = V ρ g

(ii) The upthrust on the body, acting upwards = V ρ_L g

(iii) The apparent weight of the body in liquid = V(ρ – ρ_L)g

(iv) The loss in weight of the body = V ρ_L g

💡 Some Related Questions

A weather forecasting plastic balloon of volume 15 m³ contains hydrogen of density 0.09 kg m^-3. The volume of an equipment carried by the balloon is negligible compared to it’s own volume. The mass of the empty balloon alone is 7.15 kg. The balloon is floating in air of density 1.3 kg m^-3. Calculate : (i) the mass of hydrogen in the balloon, (ii) the mass of hydrogen and balloon, (iii) the total mass of hydrogen, balloon and equipment if the mass of equipment is x kg, (iv) the mass of air displaced by balloon and (v) the mass of equipment using the law of floatation.

The density of ice is 0.92 g cm^-3 and that of sea water is 1.025 g cm^-3. Find the total volume of an iceberg which floats with it’s volume 800 cm³ above water.

A wooden block floats in water with two-third of it’s volume submerged. (a) Calculate the density of wood. (b) When the same block is placed in oil, three-quarter of it’s volume is immersed in oil. Calculate the density of oil.

A piece of wood of uniform cross section and height 15 cm floats vertically with it’s height 10 cm in water and 12 cm in spirit. Find the density of (i) wood and (ii) spirit.

If the density of ice is 0.9 g cm^-3, what portion of an iceberg will remain below the surface of water in a sea? (Density of sea water = 1.1 g cm^-3)

A piece of wax floats on brine. What fractions of it’s volume is immersed?
Density of wax = 0.95 g cm^-3,
Density of brine = 1.1 g cm^-3

A wooden cube of side 10 cm has mass 700 g. What part of it remains above the water surface while floating vertically on the water surface?

A block of wood of mass 24 kg floats on water. The volume of wood is 0.032 m³.
Find —
(a) the volume of block below the surface of water,
(b) the density of wood.
(Density of water = 1000 kg m^-3)

A rubber ball floats on water with it’s 1/3^rd volume outside water. What is the density of rubber ?

Explain the following: A ship submerges more as it sails from sea water to river water.