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question_answer1) A liquid is kept in a cylindrical vessel which is rotated about its axis. The liquid rises at the sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev \[{{s}^{-1}}\], find the difference in height of the liquid at the centre of vessel and its sides (in m)
question_answer2) A solid hemisphere is just pressed below the liquid, the value of \[\frac{{{F}_{1}}}{{{F}_{2}}}\] is ( where \[{{F}_{1}}\]and \[{{F}_{2}}\]are the hydrostatic forces acting on the curved and flat surfaces of the hemisphere) (Neglect atmospheric pressure)
question_answer3) A solid cone of height 25 cm and base diameter 25 cm floats in water with its vertex downwards such that 20 cm of its axis is immersed. Find the additional weight (in kg) that must be placed at the centre of the base such that the cone now is completely immersed in water
question_answer4) Two identical holes each of cross-sectional area \[{{10}^{-3}}{{m}^{2}}\]are made on the opposite sides of a tank containing water as shown in the figure. As the water comes out of the holes, the tank will experience a net horizontal force of 20 N. find the difference in height (in m) between the holes A and B.
question_answer5) A cylindrical vessel of cross-sectional area\[1000c{{m}^{2}}\], is fitted with a frictionless piston of mass 10 kg, and filled with water completely. A small hole of cross-sectional area\[10m{{m}^{2}}\]is opened at a point 50 cm deep from the lower surface of the piston. Find the velocity of efflux from the hole. (in m/s)
question_answer6) A uniformly tapering vessel shown in Fig. is filled with liquid of density\[900\text{ }kg/{{m}^{3}}\]. find the force that acts on the base of the vessel due to liquid is (take\[g=10m/{{s}^{2}}\]) (in N)-
question_answer7) The density of ice is 0.9 g/c.c. and that of sea water is 1.1 g/c.c. An ice berg of volume V is floating in sea water. The fraction of ice berg above water level is\[\frac{2}{N}\]. Find value of N.
question_answer8) A piece if steel floats in mercury. The specific gravity of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece some water is filled above the mercury. What part of the piece is inside the mercury?
question_answer9) A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of g/4, the fraction of volume immersed in the liquid will be?
question_answer10) A vertical jet of water coming out of a nozzle with velocity 20 m/s supports a plate of mass M stationary at a height\[h=15\text{ }m\], as shown in the figure. If the rate of water flow is 1 litre per second, find the mass of the plate is: (in kg) (Assume the collision to be inelastic)
question_answer11) A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of\[g/3\]. The fraction of volume immersed in the liquid will be-
question_answer12) A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes \[{{T}_{1}}\]time to decrease the height of water to\[H/\eta \], \[\left( \eta >1 \right)\]and it takes \[{{T}_{2}}\]time to take out the rest to water. If \[{{T}_{1}}={{T}_{2}}\], the value of \[\eta \]is:
question_answer13) Figure shows a siphon, the vessel area is very large as compared to cross section of tube. Tube has a uniform cross section, its lower end is 6m below the surface of water. What is maximum height H (in m) of the upper end for siphon to work? Take density of water\[={{10}^{3}}kg/{{m}^{3}}\], atmospheric pressure\[={{10}^{5}}N/{{m}^{2}}.\]
question_answer14) A cylindrical vessel open at the top is 20 cm high and 10 cm in diameter. A circular hole whose cross-sectional area 1 \[c{{m}^{2}}\]is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate\[100c{{m}^{3}}{{s}^{-1}}\]. Find the height of water in the vessel under steady state in cm.
question_answer15) A small wooden bell of density \['\rho '\]is immersed in water of density \[\sigma \]to depth h then released. The height H above the surface of water up to which the ball jumps out of water is \[\left( \frac{\sigma }{\rho }-\frac{n}{2} \right)\]h. Value of n is (Neglect the effect of viscosity and surface tension and assume all quantities in SI unit)
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