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maria [59]
2 years ago
15

A 3.0-cm-diameter tube is held upright and filled to the top with mercury. The mercury pressure at the bottom of the tube − the

pressure in excess of atmospheric pressure-is 48 kPa. How tall is the tube?
Physics
1 answer:
Lesechka [4]2 years ago
3 0

Answer:

Given a tube of diameter d, = 3cm = 0.03m

Pressure Balance

Mercury pressure at the tube bottom Pₓ = Pa + ρgh

where

Pa = Atmospheric pressure = 101kpa

ρ = Density of mercury = 13,546kg/m3

g = acceleration due to gravity

h = height of the tube?

Given

Bottom pressure in excess of the atmospheric pressure = 48kPa = Pₓ - Pa

Therefore, 48kPa = ρgh

h = 48(kN/m2)/ρg

h = 48,000kgms⁻²m⁻²/(13546kgm⁻³ x 9.81ms⁻²)

h = 0.36m

the tube is 36cm tall

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8 0
2 years ago
When two resistors are wired in series with a 12 V battery, the current through the battery is 0.33 A. When they are wired in pa
MA_775_DIABLO [31]

Answer:

If R₂=25.78 ohm, then R₁=10.58 ohm

If R₂=10.57 then R₁=25.79 ohm

Explanation:

R₁ = Resistance of first resistor

R₂ = Resistance of second resistor

V = Voltage of battery = 12 V

I = Current = 0.33 A (series)

I = Current = 1.6 A (parallel)

In series

\text{Equivalent resistance}=R_{eq}=R_1+R_2\\\text {From Ohm's law}\\V=IR_{eq}\\\Rightarrow R_{eq}=\frac{12}{0.33}\\\Rightarrow R_1+R_2=36.36\\ Also\ R_1=36.36-R_2

In parallel

\text{Equivalent resistance}=\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\\\Rightarrow {R_{eq}=\frac{R_1R_2}{R_1+R_2}

\text {From Ohm's law}\\V=IR_{eq}\\\Rightarrow R_{eq}=\frac{12}{1.6}\\\Rightarrow \frac{R_1R_2}{R_1+R_2}=7.5\\\Rightarrow \frac{R_1R_2}{36.36}=7.5\\\Rightarrow R_1R_2=272.72\\\Rightarrow(36.36-R_2)R_2=272.72\\\Rightarrow R_2^2-36.36R_2+272.72=0

Solving the above quadratic equation

\Rightarrow R_2=\frac{36.36\pm \sqrt{36.36^2-4\times 272.72}}{2}

\Rightarrow R_2=25.78\ or\ 10.57\\ If\ R_2=25.78\ then\ R_1=36.36-25.78=10.58\ \Omega\\ If\ R_2=10.57\ then\ R_1=36.36-10.57=25.79\Omega

∴ If R₂=25.78 ohm, then R₁=10.58 ohm

If R₂=10.57 then R₁=25.79 ohm

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<u>Answer:</u>

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I am assuming this is a true or false question, to which the answer would be True.

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