Properties of Matter 3 Question 4
10. If the radius of the opening of the dropper is $r$, the vertical force due to the surface tension on the drop of radius $R$ (assuming $r«R$ ) is
(a) $2 \pi r T$
(b) $2 \pi R T$
(c) $\frac{2 \pi r^{2} T}{R}$
(d) $\frac{2 \pi R^{2} T}{r}$
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Answer:
Correct Answer: 10. 500
Solution:
- From continuity equation
Applying Bernoulli’s theorem at 1 and 2
$$ \begin{aligned} & p _2+\frac{1}{2} \rho v _2^{2}=p _1+\frac{1}{2} \rho v _1^{2} \\ & \therefore \quad p _2=p _1+\frac{1}{2} \rho\left(v _1^{2}-v _2^{2}\right) \\ & =\left(2000+\frac{1}{2} \times 10^{3}(1-4)\right) \\ & \therefore \quad p _2=500 Pa \end{aligned} $$
