CTET Paper II (Mathematics and Science) 4 Jan 2022 Solved Paper

Concept:Water pressure at a hole depends on the depth from the water surface. The speed of efflux is given by Torricelli’s law: $v = \sqrt{2gh}$, where $h$ is the depth. The horizontal range of the water jet is proportional to $\sqrt{\text{depth} \times \text{height of hole above ground}}$.Explanation:Each cylinder has water filled up to 20 cm from the bottom. Hole A is at 5 cm from bottom → depth from surface = 15 cm, height above ground = 5 cm.Hole B is at 8 cm → depth = 12 cm, height = 8 cm.Hole C is at 10 cm → depth = 10 cm, height = 10 cm.Hole D is at 12 cm → depth = 8 cm, height = 12 cm.Range $\propto \sqrt{\text{depth} \times \text{height}}$.For A: $\sqrt{15 \times 5} = \sqrt{75} \approx 8.66$; B: $\sqrt{12 \times 8} = \sqrt{96} \approx 9.80$; C: $\sqrt{10 \times 10} = \sqrt{100} = 10$; D: $\sqrt{8 \times 12} = \sqrt{96} \approx 9.80$.The product is maximum for C (10 cm hole), so water from cylinder C travels the farthest.Answer:C