When at rest, a liquid stands at the same level in the tubes shown in figure. But as indicated a height difference h occurs when the system is given an acceleration a towards the right. Here, h is equal to

Options

A. ` (aL ) /(2 g ) `
B. ` (gL ) /(2a ) `
C. ` (gL ) /(a) `
D. ` (aL )/(g ) `

Answer

D

Explanation

For the liquid in bottom horizontal portion, net horizontal force
` F = (P _ 1 - P _ 2 ) A = rho ghA , m = rho LA , F = m xx a rArr rho ghA = rho LA a rho h = (a L )/(g) `