d
Angle of contact between mercury and soda lime glass, \(\theta=140^{\circ}\)

Radius of the narrow tube, \(r=1 mm =1 \times 10^{-3} m\)

Surface tension of mercury at the given temperature, \(s=0.465 N m ^{-1}\)

Density of mercury, \(\rho=13.6 \times 10^{3} kg / m ^{3}\)

Dip in the height of mercury \(=h\)

Acceleration due to gravity, \(g=9.8 m / s ^{2}\)

Surface tension is related with the angle of contact and the dip in the height as

\(s=\frac{h \rho g r}{2 \cos \theta}\)

\(\therefore h=\frac{2 s \cos \theta}{r \rho g}\)

\(=\frac{2 \times 0.465 \times \cos 140}{1 \times 10^{-3} \times 13.6 \times 10^{3} \times 9.8}\)

\(=-0.00534 m\)

\(=-5.34 mm\)

Here, the negative sign shows the decreasing level of mercury. Hence, the mercury level dips by \(5.34\; mm\)