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Date November 2016 Marks available 3 Reference code 16N.3.HL.TZ0.13
Level Higher level Paper Paper 3 Time zone Time zone 0
Command term Calculate Question number 13 Adapted from N/A

Question

A solid cube of side 0.15 m has an average density of 210 kg m–3.

(i) Calculate the weight of the cube.

(ii) The cube is placed in gasoline of density 720 kg m–3. Calculate the proportion of the volume of the cube that is above the surface of the gasoline.

[3]
a.

Water flows through a constricted pipe. Vertical tubes A and B, open to the air, are located along the pipe.

Describe why tube B has a lower water level than tube A.

[3]
b.

Markscheme

i
Fweight = «ρgVcube = 210×9.81×0.15=» 6.95«N»

ii
Fbuoyancy = 6.95 = ρgV gives = 9.8×10−4

\(\frac{{9.8 \times {{10}^{ - 4}}}}{{{{\left( {0.15} \right)}^3}}}\)=0.29 so 0.71 or 71% of the cube is above the gasoline

Award [2] for a bald correct answer.

a.

«from continuity equation» v is greater at B
OR
area at B is smaller thus «from continuity equation» velocity at B is greater

increase in speed leads to reduction in pressure «through Bernoulli effect»

pressure related to height of column
OR
p=\(\rho \)gh 

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics) » B.3 – Fluids and fluid dynamics (HL only)

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