Properties Of Matter Ques 13
- The buoyancy force acting on the gas bubble is (Assume $R$ is the universal gas constant)
(2008, 4M)
(a) $\rho_l n R g T_0 \frac{\left(p_0+\rho_{l g} H\right)^{2 / 5}}{\left(p_0+\rho_l g y\right)^{2 / 5}}$
(b) $\frac{\rho_l n R g T_0}{\left(p_0+\rho_l g H\right)^{2 / 5}\left[p_0+\rho_l g(H-y)\right]^{3 / 5}}$
(c) $\rho_l n R g T_0 \frac{\left(p_0+\rho_l g H\right)^{3 / 5}}{\left(p_0+\rho_l g y\right)^{8 / 5}}$
(d) $\frac{\rho_l n R g T_0}{\left(p_0+\rho_l g H\right)^{3 / 5}\left[p_0+\rho_l g(H-y)\right]^{2 / 5}}$
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Answer:
Correct Answer: 13.( b )
Solution:
- Buoyancy force
$ F=\text { (volume of bubble) }\left(\rho_i\right) g=\left(\frac{n R T_2}{p_2}\right) \rho_i g $
Here, $\quad T_2=T_0\left[\frac{p_0+\rho_c g(H-y)}{p_0+\rho_l g h}\right]^{2 / 5}$
and $\quad p_2=p_0+\rho_l g(H-y)$
Substituting the values, we get
$ F=\frac{\rho_l n R g T_0}{\left(p_0+\rho_l g H\right)^{2 / 5}\left[p_0+\rho_l g(H-y)\right]^{3 / 5}} $
$\therefore$ Correct option is (b)
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