Question 61 of 192

Two narrow bores of diameter $5.0mm$ and $8.0mm$ are joined together to form a $U-$shaped tube open at both ends. If this $U-$tube contains water, what is the difference in the level of two limbs of the tube.
[Take surface tension of water $T=7.3\times {10}^{-2}N{m}^{-1}$, angle of contact $=0,g=10{ms}^{-2}$ and density of water$\left.=1.0\times {10}^{3}kg{m}^{-3}\right]$

A$5.34mm$B$3.62mm$C$2.19mm$D$4.97mm$

Show answer and solution▾

Answer: (C) $2.19mm$

${P}_{0}-\dfrac{2T}{{R}_{1}}+{h}_{1}\rho g={P}_{0}-\dfrac{2T}{{R}_{2}}+{h}_{2}\rho g$
$\left({h}_{1}-{h}_{2}\right)\rho g=2T\left[\dfrac{1}{2.5\times {10}^{-3}}-\dfrac{1}{4\times {10}^{-3}}\right] \Rightarrow {h}_{1}-{h}_{2}=2.19mm$