Grade 12th passMechanics

The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 10^4. The height of the hill is
A) 250 m
B) 2.5 km
C) 1.25 km
D) 750 m

Sahani Kumar

7 Years agoGrade 12th pass

4 Answers

Arun

7 Years ago

Dear student

I am getting my answer as 2500 m or 2.5 km

Hence option B is correct.

Regards

Arun (askIITians forum expert)

Sahani Kumar

7 Years ago

Please explain me how you did it. Please plz........I want it's solution urgently. Sir I will be so much thankful to you.

Sarang

7 Years ago

Pressure difference between sea level and the hill would be

dP1 = dh1 X ρm X g (1)

where dh = h1 (sea level mercury height = 75 cm) - h2 (hill top mercury height = 50 cm)

ρm is the density of mercury

and the pressure difference in atmospheric pressure would be

dP2 = dh2 X ρa X g (2)

where dh2 is the height of the hill, ρa is the density of air

now, we know that (1) = (2), so

dh1 X ρm X g = dh2 X ρa X g

by substituting appropriate values and rearranging, we get

dh2 = 0.25 X (ρm/ ρa) = 0.25 X 104 m

or dh2 = 2500 m

thus, the height of the hill is

dh2 = 2500m = 2.5 km

Sarang

7 Years ago

B is correct answer

Correct option B

Explanation in answer 1

Sorry for 2 answers ….

Regards....

Sarang

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The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 10^4. The height of the hill isA) 250 m B) 2.5 kmC) 1.25 km D) 750 m

Sahani Kumar

4 Answers

Arun

Sahani Kumar

Sarang

Sarang

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The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 10^4. The height of the hill is
A) 250 m
B) 2.5 km
C) 1.25 km
D) 750 m

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21
31
41