Question

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 

Solution

Correct option is

7.2 g cm-3

 

Let V be the volume of the sphere and  its density. From the principle of flotation, we have

    Weight of sphere = Weight of displaced oil + Weight of                                     

                                                                            displaced mercury   

  

.

SIMILAR QUESTIONS

Q1

A cylindrical jar of cross-sectional area 0.01 m2 is filled with water to a height of 50 cm. It carries a tight-fitting piston of negligible mass. What is the pressure at the bottom of the jar when a mass 1 kg is placed on the piston? Take g = 10 ms–2.

Q2

A hydraulic lift is used to lift a car of mass 3000 kg. The cross-sectional area of the lift on which the car is supported is . What is the pressure on the smaller piston, if both the pistons are at the same horizontal level?

Take g =10 ms–2

Q3

A spherical ball of radius  and 104 kg/m3 falls freely under gravity through a distance h before entering a tank of water. If after entering the water the velocity of the ball does not change, find h. The viscosity of water is .  

Q4

A ring is cut from a platinum tube of 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from a pan of a balance so that it comes in contact with the water in a glass vessel. What is the surface tension of water is an extra 3.97 g weight is required to pull it away from water? (g = 980 cm/s2)

                                                           

Q5

What is the pressure on the smaller piston if the bigger piston is 5 m above the smaller piston. The density of oil filling the hydraulic machine is 800 kg m–3.

Q6

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) 

Q7

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  

Q8

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   

Q9

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.  

Q10

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