A `U`-tube of base length `l` filled with the same volume of two liquids of densities `rho` and `2rho` is moving with an acceleration `'a'` on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height `h` is given by

Options

A. ` (a)/(2g ) 1 `
B. ` (3a )/(2g ) 1 `
C. ` ( a )/(g) 1 `
D. ` (2a )/(3g) 1 `

Answer

B

Explanation

` P_1 = rho gh + P_0 " " `…(i)
, ` P_2 - P_1 = rho a xx (l)/(2) " " `…(ii)
and ` P_3- P_2 = 2 rho xx a xx (l)/(2) " " …(iii)`
From (i) , (ii) and (iii) ` P_2 = rho gh + P_0 + rho a (l)/(2) `
` P_3 = rho gh + P_0 xx rho a (l)/(2) + 2 rho xx a (l)/(2) " " ...(iv) `
`P_3 = 2 rho gh + P_0 " " ...(v) `
From (iv) and (v) `rho gh = (3 rho al )/ (2) , h = (3al ) /(2g ) `