Water flows through the tube shown in figure. The areas of cross section of the wide and the narrow portions of the tube are `5cm^2 and 2cm^2` respectively. The rate of flow of water through the tube is `500 cm^3s^-1` . Find the difference of mercury levels in the U-tube.

Answer

A, C

Explanation

Given Rate of Glow `=500cm^3/sec`
`rarrv_A=(500/5)=100cm/sec`
`V_Aa_A=V_Ba_B`
`rarr v_A/v_B=a_B/a_A=2/5`
`rarr 5v_A=2v_B`
`rarr v_B=(5/2)v_A`…………i
`rarr 1/2rhov_A^2+rhogh_A+pA=1/2 rhov_B^2+rhogh_B+p_B`
`rarr p_A-p_B=1/2[p(v_B^2-v_A^2)]`
`rarr hxx13.6xx980=1/2xx1xx21/4(100)^2`
[Using i]
[because `p_A-p_B=?]`
`rarr h=(21xx(100)^2)/(2xx13.6xx980xx4)`
`=1.969cm`