A cubical steel block floats on mercury erectly. If each side of the cube is 10 cm, (i) how much of the body is above the mercury surface? (ii) If water is poured over mercury and it just covers the upper surface of the cube, then what will be the depth of the water column? Densities of steel and mercury are `7.8g*cm^(-3)and13.6g*cm^(-3)` respectively.
Text Solution
Verified by Experts
(i) Suppose x cm of the cube remains immersed in mercury. So, according to the condition of floatation, volume of the cube `xx` density of the material of the cube = volume of mercury displaced `xx` density of mercury `therefore" "10^(3)xx7.8=10^(2)xx x xx13.6or,x=78/13.6=5.74` `therefore" "` (10 - 5.74) = 4.26 cm height of the cube remains above mercury. (ii) Let the length of the cube that ramains in water be h cm and that in mercury be (10 - h) cm. `therefore` According to the condition of floatation, volume of the cube `xx` density of the material of the cube = volume of displaced water `xx` density of water + volume of displaced mercury `xx` density of mercury `therefore" "10^(3)xx7.8=10^(2)xxhxx1+10^(2)xx(10-h)xx13.6` or, `78=h+(10-h)xx13.6or,h=58/12.6=4.6` `therefore" "` Depth of the water column = 4.6 cm.
Topper's Solved these Questions
HYDROSTATICS
CHHAYA PUBLICATION|Exercise SECTION RELATED QUESTIONS|12 Videos
HYDROSTATICS
CHHAYA PUBLICATION|Exercise HIGHER ORDER THINKING SKILL (HOTS) QUESTIONS|37 Videos
FRICTION
CHHAYA PUBLICATION|Exercise CBSE SCANNER|7 Videos
KINETIC THEORY OF GASES
CHHAYA PUBLICATION|Exercise CBSE Scanner|9 Videos
Similar Questions
Explore conceptually related problems
An iceberg is floating on sea water. What part of it remains above water? The densities of ice and sea water are 0.918g*cm^(-3)and1.03g*cm^(-3) respectively.
Each side of an iron cube is 5 cm. This cube floats on mercury. What height of the cube remains above the surface of mercury? To cover the cube, if water is poured over mercury, then what will be the height of the water column? The density of iron is 7.2g*cm^(-3) and the density of mercury is 13.6g*cm^(-3) .
A piece of iron is floating in mercury. If 5/9 part of the piece remains below mercury, then what will be its density? The density of mercury = 13.59g*cm^(-3)
An air bubble of diameter 1 mm is formed at the bottom of a lake and when it rises to the surface of the water, its diameter becomes 2 mm. If the atmospheric pressure is 760 cm of mercury, then find the depth of the lake. (Density of mercury = 13.6g*cm^(-3) )
When an air bubble rises from the bottom of a sea its volume increases to 4 times its initial value. IF the atmospheric pressure is 76 cmHg and the temperatures at the bottom and the surface of the sea are the same. Then what will be the depth of the sea? Density of mercury= 13.6 g.cm^-3 .
A U-tube of uniform cross-section contains some mercury. If water is poured into one of the limbs up to a height of 13.4cm, then find the rise in the mercury level in the other limb. The density of mercury = 13.4g*cm^(-3) .
Mercury is poured into a U-tube of uniform bore such that the level of mercury remains 20 cm below the open ends in both arms. Now, one arm is filled completely with water and the other arm with kerosene. Calculate the lengths of the water column and the kerosene column. The specific gravities of kerosene and mercury are 0.8 and 13.6 resspectively.
A vessel contains mercury and water. An iron cylinder just floats vertically in that vessel. What is the ratio of the immersed parts of the cylinder in water and in mercury? The density of mercury = 13.6g*cm^(-3) and the density of iron = 7.78g*cm^(-3) .
Calculate the pressure at the bottom of a fresh water lake of depth 10 m. The atmospheric pressure = 76 cm of mercury and the density of mercury = 13.6g*cm^(-3) .
When a body of mass 200 g is placed on a wooden cube, the cube floats completely immersed in water. When the body is removed, the cube floats up 2 cm above the surface of the water. What is the volume of the cube?
