text: # 50 gm of oven dried soil of five sizes shown in the table is taken for hydrometer analysis and 1000 cc of suspension is prepared and filled in a jar u
  
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  50 gm of oven dried soil of five sizes shown in the table is taken for hydrometer analysis and 1000 cc of suspension is prepared and filled in a jar up to 30 cm height.
  
   Particle size (mm) Weight (gm) 0·06 6 0·05 20 0·03 15 0·015 5 0·004 4
  
  If the specific gravity of soil solids is 2.7 and viscosity of soil water suspension is 1× 10-6 kN-sec/m2, the time required for all the particles to settle to the bottom of the jar is
  
  1. 2 hr 16 min
  2. 5 hr 37 min
  3. 11 hr 55 min
  4. 23 hr 50 min
  
  ## 1 Answer
  
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  Correct Answer - Option 2 : 5 hr 37 min
  
  Concept
  
  Given,
  
  Height of jar = 30 cm
  
  From stokes law
  
  We know the velocity of settling particle is
  
  ${V_s} = \frac{{{\gamma _w} \times {d^2} \times \left( {G - 1} \right)}}{{18 \times \mu }}$
  
  Where,
  
  γw is the unit weight of water
  
  d is the diameter of the particle
  
  G is the specific gravity of the particle
  
  μ is the viscosity of the fluid
  
  Note: If the lighter particle from the group of particles settles at the bottom that means every particle is settled at the bottom.
  
   Particle size (mm) Weight (gm) 0·06 6 0·05 20 0·03 15 0·015 5 0·004 4
  
  ∴ Here diameter (d) = 0.004 mm is taken from the group
  
  $Time\;required\;for\;settling\;of\;all\;particle = \frac{{Height\;of\;water\;level\;in\;jar}}{{Settling\;Velocity\;}}$
  
  $t = \frac{{30 \times {{10}^{ - 2}}}}{{14.284 \times {{10}^{ - 6}}}}$
  
  = 20215 sec
  
  = 5.61 hr
  
  = 5 hr 37 min
  
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