Question

A piece of metal floats on mercury. The coefficient of volume expansion of the metal and mercury are  respectively. If the temperature of both mercury and metal are increased by an amount , by what factor the fraction of the volume of the metal submerged in mercury changes?

Solution

Correct option is

In case of floatation  .     

  

if with change in temperature new fraction is , the factor by which the fraction of submerged volume of metal will change will be 

          

which in the light of eq. (1) becomes  

          

Now as with rise in temperature density varies according to the relation

           

SIMILAR QUESTIONS

Q1

 

If a room has dimensions , what is the mass of air in the room if density of air at NTP is 1.3 kg/m3?

[Density of water is 103 kg/m3 and g = 10 m/s2]

Q2

What force  does water exert on the base of a house tank of base area 1.5 m2 when it is filled with water up to a height of 1 m? [Density of water is 103 kg/m3 and g = 10 m/s2

Q3

When equal volumes of two metals are mixed together, the specific gravity of alloy is 4. When equal masses of the same two metals are mixed together, the specific gravity of the alloy is 3. Calculate the specific gravity of each metal.    

Q4

An open end wide tube is immersed vertically in mercury in such a way that a length 0.05 m extends above the mercury level. The open end of the tube is then closed and the tube is raised further by 0.43 m. Calculate the length of the air column above the mercury level in the tube.

                                                                         

Q5

 

A balloon filled with hydrogen has a volume of 1 m3 and its mass is 1 kg. What would be the volume of block of a very light material which it can just lift?

[Density of material of block is 91.3 kg/m3 and that of air is 1.3 kg/m3]  

Q6

A certain block weighs 15 N in air. It weighs 12 N when immersed in water. When immersed in another liquid, it weighs 13 N? Calculate the relative density of (a) the block (b) the other liquid.

Q7

A piece of copper having an internal cavity weighs 264 g in air and 221 g in water. Find the volume of the cavity. Density of copper is 8.8 g/cc.

Q8

A piece of brass (alloy of copper and zinc) weighs 12.9 g in air. When completely immersed in water it weighs 11.3 g. what is the mass of copper contained in the alloy? Specific gravities of copper and zinc are 8.9 and 7.1 respectively.    

Q9

In English the phrase ‘tip of the iceberg’ is used to mean a small visible fraction of something that is mostly hidden. For a real iceberg what is this fraction if the density of sea water is 1.03 g/cc and that of ice is 0.92 g/cc?

Q10

A block of wood floats in water with two-thirds of its volume submerged. In oil the block floats with 0.90 of its volume submerged. Find the density of (a) wood and (b) oil, if density of water is 103 kg/m3