The radii of the two columns in U tube are r1 and r2. When a liquid of density ρ (angle of contact is 0°) is filled in it the level difference of liquid in two arms is h. The surface tension of liquid is (g = acceleration due to gravity)

Question

The radii of the two columns in U tube are r1 and r2. When a liquid of density ρ (angle of contact is 0°) is filled in it the level difference of liquid in two arms is h. The surface tension of liquid is (g = acceleration due to gravity) (A) (ρ ghr1r2/2(r2-r1)) (B) (ρ gh(r1-r2)/2r1r2) (C) (2(r2-r1)/ρ ghr1r2) (D) (ρ gh/2 (r2-r1))

Tardigrade Admin · Accepted Answer

Let h1, h2 be the heights to which liquid rises in two columns of radii r1 and r2 respectively. Then h1=(2S cos 0°/r1ρ g)=(2S/r1ρ g) where s is the surface tension of liquid. and h2=(2S cos 0°/r2 ρ g)=(2S/r2 ρ g) ∴ Difference in levels of liquid in two arms of U tube is h=h1-h2=(2S/ρ g) [(1/r1)-(1/r2)] =2S ((r2-r1)/r1r2ρ g) S=(r1r2 ρ gh/2 (r2-r1))

Q. The radii of the two columns in $U$ tube are $r_{1}$ and $r_{2}$ . When a liquid of density $ρ$ (angle of contact is $0^{\circ}$ ) is filled in it the level difference of liquid in two arms is $h$ . The surface tension of liquid is ( $g$ = acceleration due to gravity)

$\frac{ρ g h r _{1} r _{2}}{2 ( r _{2} - r _{1} )}$

$\frac{ρ g h ( r _{1} - r _{2} )}{2 r _{1} r _{2}}$

$\frac{2 ( r _{2} - r _{1} )}{ρ g h r _{1} r _{2}}$

$\frac{ρ g h}{2 ( r _{2} - r _{1} )}$

Q. The radii of the two columns in U tube are r1​ and r2​. When a liquid of density ρ (angle of contact is 0∘) is filled in it the level difference of liquid in two arms is h. The surface tension of liquid is (g = acceleration due to gravity)

2(r2​−r1​)ρghr1​r2​​

2r1​r2​ρgh(r1​−r2​)​

ρghr1​r2​2(r2​−r1​)​

2(r2​−r1​)ρgh​

Q. The radii of the two columns in $U$ tube are $r_{1}$ and $r_{2}$ . When a liquid of density $ρ$ (angle of contact is $0^{\circ}$ ) is filled in it the level difference of liquid in two arms is $h$ . The surface tension of liquid is ( $g$ = acceleration due to gravity)

$\frac{ρ g h r _{1} r _{2}}{2 ( r _{2} - r _{1} )}$

$\frac{ρ g h ( r _{1} - r _{2} )}{2 r _{1} r _{2}}$

$\frac{2 ( r _{2} - r _{1} )}{ρ g h r _{1} r _{2}}$

$\frac{ρ g h}{2 ( r _{2} - r _{1} )}$