Properties Of Matter Ques 4
- Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) true?
(2018 Adv.)
(a) The resistive force of liquid on the plate is inversely proportional to $h$
(b) The resistive force of liquid on the plate is independent of the area of the plate
(c) The tangential (shear) stress on the floor of the tank increases with $u_0$
(d) The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid
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Answer:
Correct Answer: 4.( a, c, d )
Solution:
Since, height $h$ of the liquid in tank is very small.
$ \Rightarrow \quad \frac{d v}{d y}=\frac{\Delta v}{\Delta y}=\left(\frac{u_0}{h}\right) \Rightarrow F_v=-(\eta) A\left(\frac{u_0}{h}\right) $
$ F_v \propto\left(\frac{1}{h}\right), F_v \propto u_0, F \propto A, F_v \propto \eta $
Statement $\mathrm{a}, \mathrm{c}$ and are correct.
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