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
(1) 4 cm
(2) 2 cm
(3) 6 cm
(4) 8 cm
​

Answer 1

Answer:

length of oil column = 9.6 cm

Explanation:

your question is incomplete. A complete question is -----> a vertical u tube of uniform cross section contains mercury in both sides.a glycerine ( density 1.3 g/c.c) column of 10 cm is introduced into one arm.Oil of density 0.8 g/c.c is poured into the other arm until the oil and glycerine are in the same horizontal level; Find the length of oil column. density of mercury= 13.6g/c.c .

solution : Let length of oil column is L.

we can write ,

pressure due to oil + pressure due to mercury = pressure due to glycerine

or,

given, density of oil = 0.8 g/cm³

density of mercury = 13.6 g/cm³

density of glycerine = 1.3 g/cm³

so, 0.8 × L + 13.6 (10 - L) = 1.3 × 10

or, 0.8L + 136 - 13.6L = 13

or, 12.8L = 123

L = 9.6 cm

hence, length of oil column = 9.6cm

Answer 2

Answer:

(2)2cm

Explanation: For 10cm of glycerine in one arm,

Pressure P(glycerine) = (1.2*g*10) dyne/cm²

Let the height of water be h in the other arm to match P(glycerine) with P(water).

P(water) = (1*g*h) dyne/cm².

At same height from bottom,

P(water) = P(glycerine)

or, 1*g*h = 1.2*g*10

or, h = 12cm

Hence water in the other arm to match P (water) with P(glycerine) is 12cm.

So, the level difference between the two free surfaces in two arms = (12-10)cm= 2cm