11. thermodynamics — Physics STD 11 Science — Question

$1.$ If the radius of the opening of the dropper is $\mathrm{r}$, the vertical force due to the surface tension on the drop of radius $R$ (assuming $\mathrm{r} \ll R$ ) is

$(A)$ $2 \pi r T$ $(B)$ $2 \pi R T$ $(C)$ $\frac{2 \pi r^2 T}{R}$ $(D)$ $\frac{2 \pi R^2 T}{r}$

$2.$ If $\mathrm{r}=5 \times 10^{-4} \mathrm{~m}, \rho=10^3 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{~T}=0.11 \mathrm{Nm}^{-1}$, the radius of the drop when it detaches from the dropper is approximately

$(A)$ $1.4 \times 10^{-3} \mathrm{~m}$ $(B)$ $3.3 \times 10^{-3} \mathrm{~m}$

$(C)$ $2.0 \times 10^{-3} \mathrm{~m}$ $(D)$ $4.1 \times 10^{-3} \mathrm{~m}$

$3.$ After the drop detaches, its surface energy is

$(A)$ $1.4 \times 10^{-6} \mathrm{~J}$ $(B)$ $2.7 \times 10^{-6} \mathrm{~J}$

$(C)$ $5.4 \times 10^{-6} \mathrm{~J}$ $(D)$ $8.1 \times 10^{-6} \mathrm{~J}$

Give the answer question $1,2$ and $3.$