If The Temperature Of The Air Does Not Vary, The Ratio Of Its Pressure To Its Density Is Almost Constant. In This Case.           ,  Where P0 and  are The Pressure And Density Of Air, Respectively At Sea Level. Show That With This Approximation, The Variation Of Air Pressure With Altitude y is Given By             , 

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Question

 

If the temperature of the air does not vary, the ratio of its pressure to its density is almost constant. In this case. 

         

Where P0 and  are the pressure and density of air, respectively at sea level. Show that with this approximation, the variation of air pressure with altitude y is given by   

         

Solution

Correct option is

 

 

  

  

  

Further, 

      

      

Therefore equation (i) can be written as, 

       

Where, 

         

Further,      

       

           

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