10.10 In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)

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Vishal Baghel | Contributor-Level 10

5 months ago

Height of the spirit column, $h_{1}$ = 12.5 + 15 cm = 27.5 cm

Height of the water column, $h_{2}$ = 10 + 15 cm = 25 cm

Density of spirit, $ρ_{1}$ = 0.8 gm/ ${c m}^{3}$

Density of water, $ρ_{2}$ = 1 gm/ ${c m}^{3}$

Density of mercury, $ρ$ = 13.6 gm/ ${c m}^{3}$

Let h be the difference between the levels of mercury in two limbs

Pressure exerted by mercury column of h height= h $ρ g$ = 13.6hg …. (i)

Difference between pressure exerted by water and spirit columns:

= $h_{2} ρ_{2} g - h_{1} ρ_{1} g = g (25 \times 1 - 27.5 \times 0.8) =$ 3g ……. (ii)

Equating equations (i) and (ii), we get

13.6hg = 3g

h = 3/13.6 = 0.221 cm

Height of the spirit column,  <math><msub><mrow><mrow><mi>h</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> = 12.5 + 15 cm = 27.5 cmHeight of the water column,  <math><msub><mrow><mrow><mi>h</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math> = 10 + 15 cm = 25 cmDensity of spirit,  <math><msub><mrow><mrow><mi>ρ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> = 0.8 gm/ <math><msup><mrow><mrow><mi>c</mi><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math>Density of water,  <math><msub><mrow><mrow><mi>ρ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math> = 1 gm/ <math><msup><mrow><mrow><mi>c</mi><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math>Density of mercury,  <math><mi>ρ</mi></math> = 13.6 gm/ <math><msup><mrow><mrow><mi>c</mi><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math>Let h be the difference between the levels of mercury in two limbsPressure exerted by mercury column of h height= h <math><mi></mi><mi>ρ</mi><mi>g</mi></math> = 13.6hg …. (i)Difference between pressure exerted by water and spirit columns:= <math><msub><mrow><mrow><mi>h</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><msub><mrow><mrow><mi>ρ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mi>g</mi><mo>-</mo><msub><mrow><mrow><mi>h</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><msub><mrow><mrow><mi>ρ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><mi>g</mi><mo>=</mo><mi>g</mi><mfenced separators="|"><mrow><mrow><mi></mi><mn>25</mn><mi></mi><mo>×</mo><mn>1</mn><mo>-</mo><mn>27.5</mn><mo>×</mo><mn>0.8</mn></mrow></mrow></mfenced><mo>=</mo><mi></mi></math> 3g ……. (ii)Equating equations (i) and (ii), we get13.6hg = 3gh = 3/13.6 = 0.221 cm

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10.10 In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)

1 Answer

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