question_answer

A cubical block is placed on a thin liquid layer of thickness\[0.2\text{ }mm\]. The load moves downward with a constant speed of \[2\text{ }cm/sec\]after the system is released. If coefficient of viscosity of liquid is \[\frac{x}{1000}Pa-\sec ,\] then x is (Take\[g=10m/{{s}^{2}}\])               '

A) 3                       

B) 5                

C) 7                       

D) 9                                 

Correct Answer: B

Solution :

   [b] By constraint relation, velocity of block is 2K As acceleration for block and disc is zero, for disc \[2T=mg\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,T=\frac{mg}{2}\] and for block \[T=f\] \[\Rightarrow \,\,\,\,\,\frac{mg}{2}=\eta A\frac{2V}{d}\Rightarrow \eta =\frac{mgd}{4AV}\] \[=\frac{20\times {{10}^{-3}}\times 10\times 0.2\times {{10}^{-3}}}{4\times {{10}^{3}}\times {{10}^{-4}}\times 2\times {{10}^{-2}}}=5\times {{10}^{-3}}NS{{m}^{-2}}\]