Q.
Consider a $U$ -shaped frame with a sliding wire of length $l$ and mass $m$ on its arm. It is dipped in a soap solution that taken out and placed in vertical position as shown in the figure. Choose a minimum value of $m$ , so that the wire does not descend (surface tension of soap solution is $S$ ):
NTA AbhyasNTA Abhyas 2022
Solution:
For wire to be in equilibrium, force due to surface tension should be equal to force due to gravity.
So, $mg=2Sl$
$\Rightarrow m=\frac{2 S l}{g}$
For mass less than $\frac{2 S l}{g}$ , wire will move upward.
So amongst the options $\frac{S l}{4 g}$ is the minimum mass.
So, $mg=2Sl$
$\Rightarrow m=\frac{2 S l}{g}$
For mass less than $\frac{2 S l}{g}$ , wire will move upward.
So amongst the options $\frac{S l}{4 g}$ is the minimum mass.