Question

A piece of ice, with a stone frozen inside it, is floating in water contained in a beaker. When the ice melts, the level of water in the beaker

Solution

Correct option is

Falls

 

Let the mass of ice be m1 and the mass of stone be m2. The mass of the displaced water is equal to . If  is the density of water, the volume of water displaced is

          

When the ice melts, additional volume of water obtained is . The stone sinks in water, and displaces a volume of water equal to its own volume, which is  is the density of stone. Thus the total volume of extra water is   

     

 V’ < V. Therefore, level of water in beaker decreases.  

SIMILAR QUESTIONS

Q1

A vertical off-shore structure is built to withstand a maximum stress of 108Pa. The structure is suitable for putting up on the top of an oil well in Bombay High at a location where the depth of the sea is less than

(Take g = 10 ms–2 and density of sea water = 1000 kgm–3) 

Q2

A tank with a square base of area 2.0 m2 is divided into two compartments by a vertical partition in the middle. There is a small hinged door of face area 20 cm2 at the bottom of the partition. Water is filled in one compartment and an acid of relative density 1.5 in the other, both to a height of 4 m. If g = 10 ms–2, the force necessary to keep to door closed is  

Q3

A cubical block of steel of each side equal to l is floating on mercury in a vessel. The densities of steel and mercury are  and . The height of the block above the mercury level is given by   

Q4

A spring balance reads 10 kg when a bucket of water is suspended from it. What will be the reading of the balance when an iron piece of mass 7.2 kg suspended by a string is immersed with half its volume inside the water in the bucket? Relative density of iron is 7.2.  

Q5

A vessel contains oil of density 0.8 gcm–3 floating over mercury of density 13.6 gcm–3. A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the sphere in gcm–3 is 

Q6

A body floats in water with 40% of its volume outside water. When the same body floats in oil, 60% of its volume remains outside oil. The relative density of oil is  

Q7

The relative density of ice is 0.9 and that of sea water is 1.125. What fraction of the whole volume of an iceberg appears above the surface of the sea?

Q8

A common hydrometer has a uniform stem graduated downwards from 0, 1, 2, ….. up to 10. When floating in pure water it reads 0 and in a liquid of relative density 1.5, it reads 10. What is the relative density of a liquid in which it reads 5?

Q9

A cubical vessel of height 1 m is full of water. What is the amount of work done is pumping water out of the vessel? Take g = 10ms–2 

Q10

The dimensions of viscosity in terms of M, L and T are