AIIMS 2018 Physics Torricelli's Theorem MCQ Question

To determine the speed of water flowing out of the hole, we apply Torricelli's theorem, which states that the speed $v$ of fluid exiting a hole under the influence of gravity is given by $v = \sqrt{2gh}$, where $h$ is the effective height of the fluid column above the hole. In this scenario, the effective height $h$ is influenced by both the water and kerosene columns, leading to the expression $h = h_1 + h_2 \left( \frac{\rho_2}{\rho_1} \right)$, where $h_1$ is the height of water and $h_2$ is the height of kerosene.

Option A is incorrect because it does not account for the different densities of the fluids. Option B mistakenly combines the heights without considering the density ratio. Option D misrepresents the relationship between the densities and heights, leading to an incorrect effective height. Thus, option C correctly incorporates the density ratio, yielding the proper effective height for calculating the exit speed of water.