A vertical U-tube of uniform cross-section contains water in both the arms. A 10 cm glycerine column (R.D. =1.2 ) is added to one of the limbs. The level difference between the two free surfaces in the two limbs. will be

Question

A vertical U-tube of uniform cross-section contains water in both the arms. A 10 cm glycerine column (R.D. =1.2 ) is added to one of the limbs. The level difference between the two free surfaces in the two limbs. will be (A) 4 cm (B) 2 cm (C) 6 cm (D) 8 cm

Tardigrade Admin · Accepted Answer

Let the difference between 2 limbs be x Pressure on the line Y Y should be same below both limbs, so ρ text glycerine × g × h=ρ text water × g ×(h+ x) ⇒ 1.2 × 10=1 ×(h +x) ⇒ 2 cm =x

Q. A vertical U-tube of uniform cross-section contains water in both the arms. A $10 c m$ glycerine column (R.D. $= 1.2$ ) is added to one of the limbs. The level difference between the two free surfaces in the two limbs. will be

4 cm

2 cm

6 cm

8 cm

Let the difference between 2 limbs be $x$
Pressure on the line $YY$ should be same below both limbs, so
$ρ_{glycerine} \times g \times h = ρ_{water} \times g \times (h + x)$
$\Rightarrow 1.2 \times 10 = 1 \times (h + x)$
$\Rightarrow 2 c m = x$

Q. A vertical U-tube of uniform cross-section contains water in both the arms. A 10cm glycerine column (R.D. =1.2 ) is added to one of the limbs. The level difference between the two free surfaces in the two limbs. will be