Sheet 03 Buoyancy, Archimedes’ Principle and Laws of Floatation.
A concrete slab weighs \(15\,Kg\) in air. When it is completely immersed in sea water, it weighs \(10\,Kg\). Calculate: the density of sea water if the volume of sea water displaced by the slab is \(\left(4.9\times10^{4}\right)\frac{kg}{m^{3}}\). Take: \(g=10\frac{m}{s^{2}}\).
An iron casting containing a number of cavities weighs \(6280\,N\) in air and \(4280\,N\) in water. If, the density of the iron casting without cavities is \(7.85\frac{g}{cm^{3}}\). Find: the total volume of all cavities in the casting. Take: \(g=10\frac{m}{s^{2}}\).
Ans: \(V_{cavities}=0.2\,m^{3}\).
A ship of mass \(1236\,ton\) floats in a sea. If, the density of the sea water is \(\left(1.03\times10^{3}\right)kg\), (a) what is the volume of sea water displaced? If, the ship enters the fresh water lake. And (b) What mass of the cargo has to be dropped so that it displaces the same volume of water? Given: Density of the fresh water is \(1000\frac{kg}{m^{3}}\).
Ans:(a) \(1200\,m^{3}\) and (b) \(36\,ton\).
The density of ice is \(917\frac{kg}{m^{3}}\). What fraction of ice lies below the water level of a sea? The density of the sea water is \(1024\frac{kg}{m^{3}}\). What fraction of iceberg do we see above the water surface? Assuming: that is has the same density as that of the ice.
Ans: \(\frac{89}{100}\) and \(\frac{11}{100}\).
A container contain water and kerosene oil. A cubical block of ice floats partly in water and partly in kerosene oil. If the relative density of ice and kerosene oil is \(0.9\) and \(0.8\) respectively. Find: The ratio of volume of ice immersed in kerosene oil to that in water.
Ans: \(\frac{V_{o}}{V_{w}}=1\).
A solid floats in water with \(\frac{2}{3}^{rd}\) of its volume below the surface of water. Calculate: the density of the solid if the density of water is \(1000\frac{kg}{m^{3}}\).
Ans: \(\rho=666.7\frac{kg}{m^{3}}\).
A piece of pure gold \(\left(\rho=19.3\frac{g}{cm^{3}}\right)\) is suspended to be hollow. It weighs \(38.250\,g\) in air and \(33.865\,g\) in water. Calculate: the volume of the hollow portion in the gold if any.
Ans: \(V_{hollow}=2.403\,cm^{3}\).
A huge three dimensional hollow rectangular box is open from top and has a base area \(3\,m^{2}\). The height of the box is \(1.5\,m\). When placed in sea water of density \(\left(1.02\times10^{3}\right)\frac{kg}{m^{3}}\), it plunges up to \(0.5\,m\) of its height under its own weight. What additional mass can be placed in it so that it just escapes sinking in to sea?
Ans: \(m=3063\,kg\).
An iron ball of density \(7.9\frac{g}{cm^{3}}\) is suspended by a thread of negligible mass from a cylinder partly submerged into water. The area of top and bottom faces of the cylinder is \(14\,cm^{2}\) and the total height of the cylinder is \(7\,cm\). if the density of the material of the cylinder is \(0.35\frac{g}{cm^{3}}\) and \(4.5\,cm\) of the height of the cylinder is inside the water. Find: the radius of the iron ball. take: \(g=10\frac{m}{s^{2}}\).
Ans: \(r=1\,cm\).
A large iceberg of cubical shape is floating in sea water. Specific gravity of ice is \(0.9\). If, \(20\,cm\) of iceberg’s height is above the surface of sea. Determine: the volume of iceberg. Given: Specific gravity of sea water is \(1.025\).
Ans: \(V_{iceberg}=4.41\,m^{3}\).
An object hangs from a spring balance. The reading of spring balance is \(40\,N\) in air, \(30\,N\) in a liquid X and \(25\,N\) in a liquid Y. If, the liquid Y is water. Find: the density of the liquid X?
Ans: \(\rho_{X}=666.7\frac{kg}{m6{3}}\).
A hot-air balloon is accelerating upwards in air. If the ratio of density of air outside to the gas filled onside the balloon is \(1.42\). Find: the acceleration assuming that the density of material of balloon is same as the gas in it. Take: \(g=10\frac{m}{s^{2}}\).
