Properties of Matter 4 Question 15

17. If the density of air is ρa and that of the liquid ρl, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

(a) ρaρl

(b) ρaρl

(c) ρlρa

(d) ρl

Passage 2

A small spherical monoatomic ideal gas bubble (γ=5/3) is trapped inside a liquid of density ρl (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T0, the height of the liquid is H and the atmospheric pressure is p0 (Neglect surface tension)

(2008,4 M)

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Answer:

Correct Answer: 17. 4Tρv2

Solution:

  1. Free body diagram of the wire is as shown in figure.

Considering the equilibrium of wire in vertical direction, we have

2Tlcosθ=λlg

 For y«a,cosθya

Substituting the values in Eq. (i), we get

T=λa2y



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