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Chapter 1: Q91PP (page 397)

How does the force the diaphragm experiences due to the difference in pressure between the lungs and abdomen depend on the abdomen’s distance below the water surface? The force (a) increases linearly with distance; (b) increases as distance squared; (c) increases as distance cubed; (d) increases exponentially with distance.

Short Answer

Expert verified

The diaphragm will experience greater force as the elephant gradually goes deep into water. The correct option is (a) the force will increase linearly with distance.

Step by step solution

01

Identification of given data

Diaphragm experiences force due to the difference in pressure between the lungs and abdomen.

02

Concept of gauge pressure

Gauge pressure is measured in terms of atmospheric pressure instead of absolute pressure. The force directly relates to the pressure. And pressure and area are inversely related.

03

Determination of the relation between force and pressure exerted on diaphragm

The gauge pressure can be given as,

pg=pghp=FA

Here, A is the area, ρis the density, h is the depth, g is the acceleration due to gravity.

From above equations, we can say that,

F=pA=(ρgh)A

Here, the force increases linearly with distance.

Thus, the diaphragm will experience greater force as the elephant gradually goes deep into water.

Hence, the correct option is (a).

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