A solid sphere, of radius R acquires a terminal velocity v 1 when falling (due to gravity) through a viscous…

A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2, when falling through the same fluid, the ratio v1v2 equals:
  1. 19
  2. 27
  3. 127
  4. 9

Solution

If R is the radius of initial drop and r is the radius of new drop, then
43πR3=27×43πr3⇒r=R3
Terminal velocity,

         vT∝r2
⇒ v1v2=R2R32=9

Asked in: MHT CET Full Test 4

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