Question

By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg (density $13.6gc{m}^{-3}$) using the straw, he can drink water from a glass up to a maximum depth of

• A. $10.2cm$
• B. $75.3cm$
• C. $13.6cm$
• D. $1.96cm$

Answer 1

The correct option is C $13.6cm$

Normal pressure is $760mmHg$ so the boy can create a depression of $10mmHg$ in his lungs.

According to the law of flotation

Weight of floating body $=$ Weight of displaced liquid

Wt. Of water displaced from glass $=$ Wt of air of lung reduced (interm of mmHg)

Wt of water displaced from glass = density of water $\left(d_1\right)\times$ volume of water displaced $\left(v_1\right)$

Wt of air reduce from lung (interm of mmHg) $=$ density of Hg $\left(d_2\right)\times$ volume of air displaced $\left(v_2\right)$

Now $d_1\times v_1=d_2\times v_2$

And $v_1=d_2\times \frac{v_2}{d_1}=13.6g/cm–3\times \frac{10mm}{1g/cm}–3=136mm=13.6cm$