Question

A 120 kg crocodile swallows gastrolithes that are 0.8% of his mass to sink to a lower level. How much would it have to increase its lung volume in mL to counteract the sinking effect? Assume that the air pressure in its lungs is not much greater than atmospheric pressure.

Answer 1

Given,

mass of the crocodile, m = 120 kg

Let the volume of lungs be V

density of water, = 1000 kg/m³

Initially,

Weight of crocodile = buoyant force

=> 120*g = *V*g

=> V = 120 /

          = 120/1000 = 0.120 m³

Now,

mass of gastrolithis, m' = 0.8%*120

                                       = (0.8/100)*120 = 0.8*1.20

                                       = 0.96 kg

Thus,

new mass of crocodile, M = 120 + 0.96

                                          = 120.96 kg

Let the new volume of lungs be V'

Thus,

Weight of the crocodile = buoyant force

=> 120.96*g = *V'*g

=> 120.96 = 1000*V'

=> V' = 120.96/1000

          = 0.12096 m³

Therefore,

Change in volume = V' - V = 0.12096 - 0.12

                              = 0.00096 m³ = 960 * 10^-6 m³

Now,

1 m³ = 10⁶ cm³

Thus, change in volume = 960 * 10^-6 *10⁶ cm³

                                        = 960 cm³

Since, 1 cm³ = 1 ml

Thus, change in volume is 960 ml.