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).
 
A spherical solid ball of volume V is made of a material of density ρ1. It is falling through a liquid of density
ρ2. (ρ2 < ρ1). [Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed ν, ie, Fviscous = –kv2 (k > 0). The terminal speed of the ball is
  1. \(\sqrt{\frac{\mathrm{Q}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}}\)
  2. \(\frac{\mathrm{V} \rho_{1}}{\mathrm{k}}\)
  3. \(\sqrt{\frac{\mathrm{y} \rho_{1}}{\mathrm{k}}}\)
  4. \(\frac{\mathrm{V}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}\)

Answer

(A) Q ( _ 1 - _ 2 ) k

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