Question

One more physics question. Brief explanation needed. ?

Answer 1

(b)

Explanation:

Let `P_A` be atmospheric pressure. Under the given condition

Pressure at the bottom of left side of tube `=P_A+(2rho)gh`
Pressure at the bottom of right side of tube `=P_A+(rho)gh`
Difference in pressures between left and right bottoms `=P_A+2rhogh-(P_A+rhogh)=rhogh`

If `A` is the uniform area of cross section of the base then
Force in the base towards right side `=rhoghA`

Using Newton's Second Law of motion this force must be `="mass of liquid in the base"xx"acceleration"`

It is given that volume of both liquids is same.
Let us assume that area of cross section of the U-tube is uniformly same throughout or at least area of cross section of both limbs is same. Since `h` is equal in both limbs, it implies that volume of both liquids in the base must be equal. This implies that the interface between the two liquids is exactly at the midpoint of base.

`:."Mass of liquids in the base"\ = [2rho(l/2)A + rho(l/2)A]`
`=>"Mass of liquids in the base"\ = 3/2rholA`

Equating two forces we get

`rhoghA=3/2rholAa`
`=>h=(3la)/(2g)`