Properties of Matter 4 Question 12

14. Two spheres P and Q for equal radii have densities ρ1 and ρ2, respectively. The spheres are connected by a massless string and placed in liquids L1 and L2 of densities σ1 and σ2 and viscosities η1 and η2, respectively. They float in equilibrium with the sphere P in L1 and sphere Q in L2

and the string being taut (see figure). If sphere P alone in L2 has terminal velocity vP and Q alone in L1 has terminal velocity vQ, then

(2015 Adv.)

(a) |vP||vQ|=η1η2

(b) |vP||vQ|=η2η1

(c) vPvQ>0

(d) vPvQ<0

Assertion and Reason

Mark your answer as

(a) If Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I

(b) If Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

(c) If Statement I is true; Statement II is false

(d) If Statement I is false; Statement II is true

Show Answer

Answer:

Correct Answer: 14. 3

Solution:

  1. Terminal velocity is given by

vT=29r2η(dρ)gvPvQ=rP2rQ2×ηQηP×(dρP)(dρQ)=(10.5)×(23)×(80.8)(81.6)=4×23×7.26.4=3



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