Question

 

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. 

Solution

Correct option is

Consider two levels at heights h and h + dh in the atmosphere from sea level. If p1 and p2 are the pressure at these heights respectively, then

    

Now as in the atmosphere with height density and so pressure is decreasing, if p1 = pp2 = p – dp.   

  

which on integration gives 

         

But as   h → ∞, p → 0, so C = 0. 

  

At sea-level h = 0, 

                     

                     

SIMILAR QUESTIONS

Q1

A piece of metal floats on mercury. The coefficient of volume expansion of the metal and mercury are  respectively. If the temperature of both mercury and metal are increased by an amount , by what factor the fraction of the volume of the metal submerged in mercury changes?

Q2

A block of wood floats in water with two-thirds of its volume submerged. In oil the block floats with 0.90 of its volume submerged. Find the density of (a) wood and (b) oil, if density of water is 103 kg/m3  

Q3

Air is streaming past a horizontal aeroplane wing such that its speed is 120 m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg/m3, find the difference in pressure between the top and bottom of the wing. If the wing is 10 m long and has an average width 2m, calculate the gross lift of the wing. 

Q4

A horizontal pipe line carries water in a streamline flow. At a point along the pipe where the cross-section area is 10 cm2, the water velocity is 1 m/s and the pressure is 2000 Pa. What is the pressure of water at another point where the cross-section area is 5 cm2?

Q5

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 

Q6

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)

Q7

The vertical section of a wing of a fan is shown below. Maximum upthrust is in

                                            

Q8

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

Q9

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?

Q10

 

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).