A glass beaker having mass 390 g and an interior volume of 500 cm3 floats on water when it is less than half filled with water. What is the density of the material of the beaker?
As the beaker floats in water when less than half filled with water, it will float just fully submerged when half filled. In this situation, mass of beaker + mass of water in it
i.e., outer volume of beaker
Now as inner volume of beaker is given to be 500 cc, so the volume of the material of beaker = 640 – 500 = 140 cc. But as mass of beaker is 390 g, so density of material of beaker
= 2.79 g/cc
Water from a tap emerges vertically downward with an initial speed of 1.0 ms–1. The cross-sectional area of the tap is 10–4 m2. Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is : (g = 10 m/s2)
Water is filled in a cylindrical container upto a height of 3 m. A hole of cross-section area a is made in the wall of the container at a height of 52.5 cm from the bottom. The cross-section area of the container is A. If a/A = 0.1, then the squire of the speed of water coming out from the hole is (g = 10 m/s2)
The vertical section of a wing of a fan is shown below. Maximum upthrust is in
The vertical of a mass ball of mass M and density d1, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d2, the viscous force acting on the ball will be
To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid passes on the side of the vessel equal to the force exerted be the liquid on the bottom of the vessel?
The density of air in atmosphere decreases with height and can be expressed by the relation:
Where is the density at sea-level, A is a constant and h is the height. Calculate the atmospheric pressure at sea-level. Assume g to be constant.
A rod of length 6 m has a mass 12 kg. It is hinged at one end at a distance of 3 m below water surface. (a) What weight must be attached to the other end of the rod so that 5 m of the rod are submerged? (b) Find the magnitude and direction of the force exerted by the hinge on the rod.
(Specific gravity of rod is 0.5).
A large block of ice 5 m thick has a vertical hole drilled through it floating in the middle of a lake. What is the minimum length of a rope required to scoop up a bucket full of water through the hole?
[RD of ice = 0.9]
A cubical block of iron 5 cm on each side is floating on mercury in a vessel. Water is poured into the vessel so that it just covers the iron block. What is the height of water column?
[RD of Hg = 13.6 and Fe = 7.2]
A block of wood weighs 12 kg and has a relative density 0.6. It is to be in water with 0.9 of its volume immersed. What weight of a metal is needed if the metal is attached below the wood?
[RD of metal = 14]