A small spherical droplet of density d is flo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For the droplet to be in equilibrium,the total upward force must equal the downward force.The forces acting on the droplet are:$1$. Buoyant force

Vedclass · Accepted Answer

$r=\sqrt{\frac{3 T}{(2 d-\rho) g}}$

Vedclass · Answer

(B) For the droplet to be in equilibrium,the total upward force must equal the downward force.The forces acting on the droplet are:$1$. Buoyant force $(B)$: $B = V_{	ext{immersed}} ho g = (\frac{1}{2} \cdot \frac{4}{3} \pi r^3) ho g = \frac{2}{3} \pi r^3 ho g$$2$. Surface tension force $(F)$: $F = T \cdot (2 \pi r)$$3$. Weight of the droplet $(mg)$: $mg = (V_{	ext{total}} d) g = (\frac{4}{3} \pi r^3) d g$Equating the forces: $B + F = mg$$\frac{2}{3} \pi r^3 ho g + 2 \pi r T = \frac{4}{3} \pi r^3 d g$Divide by $\pi r$:$\frac{2}{3} r^2 ho g + 2 T = \frac{4}{3} r^2 d g$Rearranging to solve for $r^2$:$2 T = \frac{4}{3} r^2 d g - \frac{2}{3} r^2 ho g$$2 T = \frac{2}{3} r^2 g (2d - ho)$$T = \frac{1}{3} r^2 g (2d - ho)$$r^2 = \frac{3 T}{(2d - ho) g}$$r = \sqrt{\frac{3 T}{(2d - ho) g}}$

$A$ small spherical droplet of density $d$ is floating exactly half immersed in a liquid of density $\rho$ and surface tension $T$. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet).

Similar Questions

Which one of the following statements is correct?

Detergents are added to water for removing dirt from clothes. Explain.

Why does the free surface of a liquid tend to contract?

If the work done in increasing the size of a soap film from $10\;cm \times 6\;cm$ to $10\;cm \times 11\;cm$ is $2 \times 10^{-4}\;J$,then the surface tension is:

The force required to take away a flat circular plate of radius $2 \ cm$ from the surface of water is $[$ Surface tension of water $= 70 \times 10^{-3} \ Nm^{-1}, \pi = \frac{22}{7} ]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module