A Wooden Stick Of Length L, Radius R and Density  has A Small Metal Piece Of Mass m (of Negligible Volume) Attached To Its One End. Find The Minimum Value Of The Mass m (in Terms Of Given Parameters) That Would Make The Stick Float Vertically In Equilibrium In A Liquid Of Density . 

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 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?

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]  

Calculate the rate of flow of glycerine of density  through the conical section of a pipe, if the radii of its ends are 0.1 m and 0.04 m and the pressure drop across its length is 10 N/m².