When an air bubble of radius r rises from the | vedclass

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

Question

(C) Let the depth of the lake be $h$. The atmospheric pressure $P_0$ is equivalent to a water column of height $H = 10 \ m$. At the bottom of the lake

Vedclass · Accepted Answer

$9.53$

Vedclass · Answer

(C) Let the depth of the lake be $h$. The atmospheric pressure $P_0$ is equivalent to a water column of height $H = 10 \ m$. At the bottom of the lake,the pressure $P_1 = P_0 + h ho g = (H + h) ho g$. At the surface,the pressure $P_2 = P_0 = H ho g$. Since the temperature is constant,we use Boyle's Law: $P_1 V_1 = P_2 V_2$. Given $V_1 = \frac{4}{3} \pi r^3$ and $V_2 = \frac{4}{3} \pi (\frac{5r}{4})^3$. Substituting the values: $(H + h) ho g 	imes \frac{4}{3} \pi r^3 = H ho g 	imes \frac{4}{3} \pi (\frac{5r}{4})^3$. $(10 + h) = 10 	imes (\frac{5}{4})^3$. $10 + h = 10 	imes \frac{125}{64} = \frac{1250}{64} = 19.53125$. $h = 19.53125 - 10 = 9.53125 \ m \approx 9.53 \ m$.

Similar Questions

What is the common name of benzene$-1,3-$diol?

In an $AC$ circuit,the current is given by $i = 5 \sin(100t - \frac{\pi}{2}) \text{ A}$ and the $AC$ potential is $V = 200 \sin(100t) \text{ V}$. Then the power consumption is $....$ watt.

Which of the following is not a class of $Bryophytes$?

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is

Vedclass Test Series

Exam Paper Generator

Online Exam Module