## Question

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

### Solution

1.5

In each case, the weight of the body is equal to the upthrust. Thus, if *V* is the volume of the body and the relative density of the liquid, we have

.

#### SIMILAR QUESTIONS

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}.

A spherical ball of radius and 10^{4} kg/m^{3} 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 .

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/s^{2})

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}.

A vertical off-shore structure is built to withstand a maximum stress of 10^{8}Pa. 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})

A tank with a square base of area 2.0 m^{2} is divided into two compartments by a vertical partition in the middle. There is a small hinged door of face area 20 cm^{2} 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

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

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.

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

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?