A column of mercury is in the middle of horizontal tube of uniform cross section closed at both ends. The pressure of the enclosed air column on either side of the mercury is 75 cm of mercury column. When the tuve is placed vertical the length air below the mercury column is `(3)/(5)` th of that above it. if length of mercury column is 10n cm. find n.

Answer

4

Explanation

`((L)/(2)-(x)/(2)-y)=(3)/(5)((L)/(2)-(x)/(2)+y)impliesy=(1)/(4)[(L)/(2)-(x)/(2)]`
`impliesP_(0)[(L)/(2)-(x)/(2)]=P_(0)^(')xx(5)/(4)[(L)/(2)-(x)/(2)]impliesP_(0)^(')=(4P_(0))/(5)`
`impliesP_(0)[(L)/(2)-(x)/(2)]=P_(0)^('')(3)/(4)[(L)/(2)-(x)/(2)]impliesP_(0)^('')=(4P_(0))/(3)`
`implies(P_(0)^('')-P_(0)^('))A=Arho_(m)gx`
`implies4xxrhomxxgxx75xx(2)/(15)=rhomgx` `impliesx=40`cm