Question

A barometer is constructed with its tube having radius 1.0 mm. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to 76 cm of mercury, what will be the height raised in the barometer tube? The contact angle of mercury with glass = 135 ° and surface tension of mercury = 0.465 N m−1. Density of mercury = 13600 kg m−3.

Answer 1

Answer :

Answer : C

Answer : CSolution :

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm,

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm h=2Tcosθrρgh=2Tcosθrρg

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm h=2Tcosθrρgh=2Tcosθrρg θ=135∘,t=0.465Nmθ=135∘,t=0.465Nm

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm h=2Tcosθrρgh=2Tcosθrρg θ=135∘,t=0.465Nmθ=135∘,t=0.465Nm h=2×465×(12√)10−3×13600×10=0.0048mh=2×465×(12)10-3×13600×10=0.0048m

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm h=2Tcosθrρgh=2Tcosθrρg θ=135∘,t=0.465Nmθ=135∘,t=0.465Nm h=2×465×(12√)10−3×13600×10=0.0048mh=2×465×(12)10-3×13600×10=0.0048m =0.48cm=0.48cm

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm h=2Tcosθrρgh=2Tcosθrρg θ=135∘,t=0.465Nmθ=135∘,t=0.465Nm h=2×465×(12√)10−3×13600×10=0.0048mh=2×465×(12)10-3×13600×10=0.0048m =0.48cm=0.48cm =capillary fault due to surface tension

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm h=2Tcosθrρgh=2Tcosθrρg θ=135∘,t=0.465Nmθ=135∘,t=0.465Nm h=2×465×(12√)10−3×13600×10=0.0048mh=2×465×(12)10-3×13600×10=0.0048m =0.48cm=0.48cm =capillary fault due to surface tension So, height raised in barometer tube

Answer : CSolution : r=1.0mm,r=1.0mm,p=76cm, θ=135∘,T=0.4654Nmθ=135∘,T=0.4654Nm h=2Tcosθrρgh=2Tcosθrρg θ=135∘,t=0.465Nmθ=135∘,t=0.465Nm h=2×465×(12√)10−3×13600×10=0.0048mh=2×465×(12)10-3×13600×10=0.0048m =0.48cm=0.48cm =capillary fault due to surface tension So, height raised in barometer tube =H−h=76−0.48=75.52cm

Answer 2

The height will be raised in the barometer tube=75.52cm

Explanation:

Radius of tube=1 mm=$1\times 10^{-3}$ m

Because $1mm=10^{-3}m$

H=76 cm=$76\times 10^{-2} m$

$1m=100 cm$

$\theta=135^{\circ}$

$T=0.465 Nm^{-1}$

$\rho=13600 kgm^{-3}$

$h=\frac{2Tcos\theta}{r\rho g$

Where T=Surface tension

$\theta$=Angle of contact

r=Radius of tube

$\rho$=Density of liquid

$g=10 m/s^2$=Acceleration due to gravity

Substitute the values then we get

$h=\frac{2\times 0.465\times cos(135)}{13600\times 10^{-3}\times 10}=-0.0048 m$

$h=0.48 cm$

Height cannot be negative .

Negative sign indicates that the level of mercury depressed.

The height will be raised in the barometer tube=H-h=$76-0.48=75.52 cm$

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