In the figure, the cross-sectional area of the smaller tube is a and that of the larger tube is `2a`. A block of mass `m` is kept in the smaller tube having the base area that of the tube. The difference between water levels of the two tubes is

Options

A. (a) ` (P _ 0 ) /( rho g ) + (m ) /(a rho )`
B. (b)` (P _ 0 )/( rho g ) + (m ) /(2 a rho ) `
C. (c)` (m)/( a rho ) `
D. (d)` (m ) /( 2 a rho ) `

Answer

C

Explanation

Pressure at the bottom level of the block, ` P = (mg )/( a) + P_ 0 `
The pressure at the same level remains same. Hence, ` (mg )/(a ) + P _ 0 = h rho g + P_ 0 rArr h = (m )/(arho ) `