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 ):

Question

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 ): <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-5qlctld910qhfw7u.jpg" /> (A) (2 S l/g) (B) (S l/g) (C) (S l/2 g) (D) (S l/4 g)

Tardigrade Admin · Accepted Answer

For wire to be in equilibrium, force due to surface tension should be equal to force due to gravity. So, mg=2Sl ⇒ m=(2 S l/g) For mass less than (2 S l/g) , wire will move upward. So amongst the options (S l/4 g) is the minimum mass.

$\frac{2 Sl}{g}$

$\frac{Sl}{g}$

$\frac{Sl}{2 g}$

$\frac{Sl}{4 g}$

For wire to be in equilibrium, force due to surface tension should be equal to force due to gravity.
So, $m g = 2 Sl$
$\Rightarrow m = \frac{2 Sl}{g}$
For mass less than $\frac{2 Sl}{g}$ , wire will move upward.
So amongst the options $\frac{Sl}{4 g}$ is the minimum mass.

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 ):

g2Sl​

gSl​

2gSl​

4gSl​

For wire to be in equilibrium, force due to surface tension should be equal to force due to gravity. So, mg=2Sl ⇒m=g2Sl​ For mass less than g2Sl​ , wire will move upward. So amongst the options 4gSl​ is the minimum mass.

$\frac{2 Sl}{g}$

$\frac{Sl}{g}$

$\frac{Sl}{2 g}$

$\frac{Sl}{4 g}$

For wire to be in equilibrium, force due to surface tension should be equal to force due to gravity.
So, $m g = 2 Sl$
$\Rightarrow m = \frac{2 Sl}{g}$
For mass less than $\frac{2 Sl}{g}$ , wire will move upward.
So amongst the options $\frac{Sl}{4 g}$ is the minimum mass.