A \(\mathrm U\text -\)shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of \(1.5\times10^{-2}~\text{N}\) (which includes the small weight of the slider). The length of the slider is \(30~\text{cm}.\) The surface tension of the film is:

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? The surface tension of mercury at that temperature (${20}^0<mspace\; width="1em"></mspace>C$) is 4.65 × 10^–1 N m^–1. The atmospheric pressure is 1.01 × 10⁵ Pa.

$\left(1\right)<mspace\; width="1em"></mspace>2.30\times {10}^5<mspace\; width="1em"></mspace>Pa$
$\left(2\right)<mspace\; width="1em"></mspace>2.01\times {10}^{5<mspace\; width="1em"></mspace>}Pa$
$\left(3\right)<mspace\; width="1em"></mspace>3.01\times {10}^5<mspace\; width="1em"></mspace>Pa$
$\left(4\right)<mspace\; width="1em"></mspace>1.01\times {10}^5<mspace\; width="1em"></mspace>Pa$

What is the excess pressure inside a bubble of soap solution of radius \(5.00~\text{mm}?\)
(Given that the surface tension of soap solution at the temperature (\(20^{\circ}\text C\)) is \(2.5\times 10^{-2}~\text{N/m}\))
1. \(10~\text{Pa}\) 
2. \(20~\text{Pa}\) 
3. \(1.06\times 10^{5}~\text{Pa}\) 
4. \(15~\text{Pa}\) 

Two narrow bores of diameters \(3.0 ~\text{mm}\) and \(6.0 ~\text{mm}\) are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? (The surface tension of water at the temperature of the experiment is \(7.3\times 10^{-2} ~\text{Nm}^{-1}\). Take the angle of contact to be zero and the density of water to be \(1.0\times 10^{3}~\text{kg m}^{-3}.\)\((g=9.8 ~\text{ms}^{-2})\)
1. \(4.95 ~\text{mm}\)
2. \(3.73 ~\text{mm}\)
3. \(8.91 ~\text{mm}\)
4. \(5.36 ~\text{mm}\)