A cylindrical tank having cross sectional area A = 0.5 m 2 is filled with two liquids of…

Physics · JEE Advanced · NTA Exams — Properties of Solids and Liquids


A cylindrical tank having cross sectional area A = 0.5 m2 is filled with two liquids of density ρ1 = 900 kg m–3 and
ρ2 = 600 kg m–3, to a height h = 60 cm each as shown in the figure. A small whole having area a = 5 cm2 is made in right vertical wall at a height y = 20 cm from the bottom. A horizontal force F is applied on the tank to tank to keep it in static equilibrium. The tank is lying on a horizontal surface. Neglect mass of cylindrical tank in comparison to mass of liquids (take g = 10 ms–2).
 
If a number of identical droplets of water, each of radius r, coalesce to form a single drop of radius R, the resulting rise in the temperature of water is given by (here ρ is the density of water, s its specific heat and σ its surface tension)
  1. \(\frac{\sigma}{\rho s}\left(\frac{1}{r}-\frac{1}{R}\right)\)
  2. \(\frac{3 \sigma}{\rho s}\left(\frac{1}{r}-\frac{1}{R}\right)\)
  3. \(\frac{\sigma}{\rho s}\left(\frac{1}{r}+\frac{1}{R}\right)\)
  4. \(\frac{3 \sigma}{\rho s}\left(\frac{1}{r}+\frac{1}{R}\right)\)

Answer

(B) 3 s ( 1 r - 1 R )

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