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**Introductory Exercise 13.1**

**Ques 1: Two vessels A and B have same base area. Equal volumes of a liquid are poured in the two vessels to different heights h _{A} and h_{B}(> h_{A}). In which vessel, the force on the base of vessel will be more.**F

Sol:

as h

Sol:

= 6.92 × 10

Sol:

Sol:

(a) When some of the gas is removed by a pump, the manometer reads as in

(b) The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.

(i) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b) in unit s of cm of mercury.

Sol:

(ii) 13.6 cm of water = 1 cm of Hg,

i.e., Hg in left limb will rise by 0.5 cm and on right limb, it will fall by 0.5 cm. Thus difference in Hg level will become 19 cm.

**Introductory Exercise 13.2**

**Ques 1: A metallic sphere floats in an immissible mixture of water (ρ _{w} = 10^{3} kg/m^{3}) and a liquid (ρL = 13.5 × 10^{3} kg/m^{3}) such that its 4/5 th volume is in water and 1/5 th volume in the liquid. Find the density of metal.**

V(ρ

⇒ ρ

Sol:

Sol:

Sol:

m = V(σ - ρ)

Sol:

Vρg + mg = Vσg

= 10

Sol:

Sol:

**Introductory Exercise 13.3**

**Ques 1. A water film is made between two straight parallel wires of length 10 cm each, and at a distance of 0.5 cm from each other. If the distance between the wires is increased by 1 mm, how much work will be done? Surface tension of water = 7.2 x 10 ^{-2} N/m.**

ΔW =F × s = 2 Tl × 0.5

= 2 × 7.2 × 10^{-2} × 10^{-1} × 10^{-3 }

= 1.44 × 10^{-5} J**Ques 2. A soap bubble of radius R has been formed at normal temperature and pressure under isothermal conditions. Compute the work done. The surface tension of soap solution is T,****Sol:**** ****Ques 3. If a drop of radius r breaks up into 27 small drops then how much will be the change in the surface energy. The surface tension of liquid is T.****Sol: **

⇒ r =3R

⇒ R = r/3 ΔS = 27 × 4pR^{2} - 4πr^{2}^{}

**Ques 4. When wax is rubbed on cloth, the cloth becomes water proof why?****Sol: **As wax seals thread capillaries which sucks water, that's why water cannot spread over cloth and cloth becomes waterproof.**Ques 5. Water at 20°C is flowing in a pipe of radius 20.0 cm. The viscosity of water at 20°C is 1.005 centipoise. If the water's speed in the centre of the pipe is 3.00 m/s, what is water's speed:(a) 10.0 cm from the centre of the pipe (half way between the centre and the walls)(b) at the walls of the pipe?**

(a) If the pipe has diameter 8.0 cm, what is the volume flow rate?

(b) What gauge pressure must the pump provide to achieve the same volume flow rate for a pipe with a diameter of 4.0 cm?

(c) For pipe in part (a) and the same gauge pressure maintained by the pump, what does the volume flow rate become if the water is at a temperature of 60°C (the viscosity of water at 60°C is 0.469 poise)

= 7.005 × 10

(b)

= 16

⇒ Δp

(c)

∴ For new value of h.

= 1.5 × 10

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