Hydrostatic weighing, or \"underwater weighing,\" is used to measure a patient\'

Question

Hydrostatic weighing, or "underwater weighing," is used to measure a patient's body composition. To do this measurement, the patient is weighed while standing on a regular scale and then weighed while immersed in water. By comparing these weights, the density and body fat percentage of a patient can be recorded. The weight of your patient on a regular scale is 600 N and while immersed in water is 90 N. The density of water is 1000 kg/m3 and assume that g = 10 m/s2.

Part B If you were to unknowingly use salt water( 1025 kg/m3) in place of fresh water, how would this affect your measurement of the patient's density? The patient's density would be measured higher than it actually is. The patients density would be measured correctly. The patient's density would be measured lower than it actually is. The patient's density would be measured as 0 kg/m3 Submit My Answers Give Up Incorrect; correct answer withheld by instructor

Explanation / Answer

given weight of patient on regular scale, W1 = 600 N

Weight of patient inside water, W2 = 90 N

density of water, rho = 1000 kg/m^3

acceleration due to gravity g = 10 m/s/s

a. let volume of human body be V

and density of human body be rhoo

then Buoyant force, B = rho*Vg

so, from force balance

W1 = W2 + B

600 - 90 = 1000*V*10

V = 0.051 m^3

so if salt water was used, then W2 = 90 N

then buoyant force will be more, so weight measured under water will decrease

now density of human body = rhoo = W1/g*V

as in this case, volume would be calculated more than it is actually, so hence the measured density would be lesser than the actual density of human body

hence option C

The patients density would be measured l;ower than what it is

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