Question

In Figure I an air column of length $l_1$, is entrapped by a column of $Hg$ of length $8\text{cm}$. In Figure II length of same air column at the same temperature is $l_2$. Then $l_1/l_2$ is?
(1 atm = $76\text{cm of}Hg$)

• A. $1+\frac{2}{19}\times \cos \theta$
• B. $1+\frac{2}{19}\times \sin \theta$
• C. $1+\frac{2}{21}\times \sin \theta$
• D. $\frac{21}{19}$

Answer 1

The correct option is B $1+\frac{2}{19}\times \sin \theta$

According to Boyle's law:
$P_1{l}_{1}a=P_2{l}_{2}a$
$P_1=76\text{cm of}Hg$
$\Rightarrow$$P_1\times l_1=(76+8\sin \theta )l_2$
So, $\frac{l_1}{l_2}=\frac{76+8\sin \theta }{76}=1+\frac{8\sin \theta }{76}$
$=1+\frac{2}{19}\sin \theta$