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

$A$ drop of liquid of density $\rho$ is floating half-immersed in a liquid of density $\sigma$ and surface tension $T = 7.5 \times 10^{-4} \, N \, cm^{-1}$. The radius of the drop in $cm$ will be: (Take: $g = 10 \, m/s^2$)

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

The free surface of a liquid has a tendency to contract. This property is called ...... .

$A$ massless inextensible string in the form of a loop is placed on a horizontal film of soap solution of surface tension $T$. If the film is pierced inside the loop and it converts into a circular loop of diameter $d$,then the tension produced in the string is ..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module