1. A rubber ball floats on water with its 1/3rd volume outside water.

What is the density of

2. A block of wood of mass 24kg 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/m³)

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

4. A piece of wax floats on brine. What fractions of its volume is immersed? Density of wax
0.95 g/cm³, density of brine = 1.1g/cm³

5. A body of volume 100cc weighs 1 kgf in air. Find: (i) its weight in water and (ii) its relative
density.5.If the density of ice is 0.9 g/cm³, what portion of an iceberg will remain below the
surface of water in a sea? (Density of sea water = 1.1 g/cm³)

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

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

8.The density of ice is 0.92 g/cm³ and that of sea water is 1.025 g/cm³.Find the total volume of
an ice berg which floats with its volume 800 cm³ above water.

9.A weather forecasting plastic balloon of volume 15m³ contains hydrogen of density
0.09kg/m³.The volume of an equipment carried by the balloon is negligible compared to its own
volume. The mass of empty balloon alone is 7.15kg. The balloon is floating in air of density 1.3
kg/m³ 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.

10.The density of copper is 8.83 g/cm³, Express it in kg/m³.

11.The relative density of mercury is 13.6. State its density in (i) C.G.S. unit (ii) S.I. unitunit.

12.The density of iron is 7.8 x 10³ kg/m³,What is its relative density?

13. The relative density of silver is 10.8. Find its density.

14. Calculate the mass of a body whose volume is 2m³ and relative density is 0.52.

15. Calculate the mass of air in a room of dimensions 4.5m x 3.5m x 2.5m if the density of air at
N.T.P. is 1.3 kg/m³

16.A piece of stone of mass 113g sinks to the bottom in water contained in a measuring
cylinder and water level in cylinder rises from 30ml to 40ml. Calculate R.D. of stone.

17. A body of volume 100cm³ weighs 1 kgf in air. Find: (i) its weight in water and (ii) its relative
density.

18. A body of mass 70kg, when completely immersed in water, displaces 20,000 cm³ of water.
Find: (i) the weight of the body in water and (ii) the relative density of material of the body.

19. A solid weighs 120 gf in air and 105 gf when it is completely immersed in water. Calculate
the relative density of solid.

20. A solid weighs 32 gf in air and 28.8 gf in water. Find: (i) the volume of solid, (ii) R.D. of solid,
and (iii) the weight of solid in a liquid of density 0.9g/cc

21.A body of volume 100cc weighs 5kgf in air. It is completely immersed in a liquid of density
1.8 x 103 kg/mc, find: (i) the upthrust due to liquid and (ii) the weight of the body in liquid.

22. A body weighs 450 gf in air and 310 gf when completely immersed in water. Find:

(i) The volume of the body,

(ii) The loss in weight of the body, and

(iii) The upthrust on the body.

State the assumption made in part (i).

23. You are provided with a hollow iron ball A of volume 15cc and mass 12g and a solid iron ball
B of mass 12g. Both are placed on the surface of water contained in a large tub. (a) Find
upthrust on each ball. (b) Which ball will sink? Give reason for your answer.(Density of iron =
8.0g/cc)

24.A solid of density 5000kg/m³ weighs 0.5kgf in air. It is completely immersed in water of
density 1000 kg/m³. Calculate the apparent weight of the solid in water.

25. Two spheres A and B, each of volume 100cm³ are placed on water (density =1.0g/cc). The
sphere A is made of wood of density 0.3g/cc and the sphere B is made of iron of density
8.9g/cc .(a) Find: (i) the weight of each sphere, and (ii) the upthrust on each sphere.

(b) Which sphere will float? Give reason.

26. The mass of a block made of a certain material is 13.5kg and its volume is 15 x 10-³m³.

(a) Calculate upthrust on the block if it is held fully immersed in water

(c) What will be the upthrust on block while floating? Take density of water = 1000 kg/m³.

27. A piece of brass weighs 175gf in air and 150 gf when fully immersed in water. The density of
water is 1.0g/cc.(i) What is the volume of the brass piece? (ii) Why does the brass piece weigh
less in water?

28.A metal cube of edge 5cm and density 9.0 g/cc is suspended by a thread so as to be
completely immersed in a liquid of density 1.2 g/cc. Find the tension in thread. (Take g = 10m/s²)
[Hint: Tension in thread = apparent weight of the cube in liquid]

29. A block of wood is floating on water with its dimensions 50cm x 50 cm x 50 cm inside water.
Calculate the buoyant force acting on the block. Take g = 9.8N/kg

30.A block of mass 3.5kg displaces 1000cc of water when fully immersed inside it. Calculate: (i)
the volume of body, (ii) the upthrust on body and (iii) the apparent weight of body in water.

31. A piece of stone of mass 113g sinks to the bottom in water contained in a measuring
cylinder and water level in cylinder rises from 30ml to 40ml. Calculate R.D. of stone.

32. A body of volume 100cc weighs 1 kgf in air. Find: (i) its weight in water and (ii) its relative
density.

33. A body of mass 70kg, when completely immersed in water, displaces 20,000 cc of water.
Find: (i) the weight of the body in water and (ii) the relative density of material of the body.

34. A solid weighs 120gf in air and 105 gf when it is completely immersed in water. Calculate
the relative density of solid.

35. A solid weighs 1.5 kgf in air and 0.9kgf in a liquid of density 1.2 x 103 kg/m³. Calculate R.D.
of solid.

36.A body weighs 20gf in air and 18 gf in water. Calculate relative density of the material of the
body.

37. A solid weighs 32 gf in air and 28.8 gf in water. Find: (i) the volume of solid, (ii) R.D. of solid,
and (iii) the weight of solid in a liquid of density 0.9g/cc.

38. A jeweler claims that he makes ornament of pure gold of relative density 19.3. He sells a
bangle weighing 25.25 gf to a person. The clever customer weighs the bangle when immersed
in water and finds that it weighs 23.075 gf in water. With the help of suitable calculations find
out whether the ornament is made of pure gold or not.

[Hint: Calculate R.D of material of bangle which comes out to be 11.6]

39. A piece of iron weighs 44.5 gf in air. If the density of iron is 8.9 x 10³ kg/m³, find the weight
of the iron piece when immersed in water.

40. A piece of stone of mass 15.1g is first immersed in a liquid and it weighs 10.9 gf. Then on
immersing the piece of stone in water, it weighs 9.7 gf. Calculate:

(a) The weight of the piece of stone in air,

(b) The volume of the piece of stone,

(c) The relative density of stone,

(d) The relative density of the liquid.