A cylindrical vessel of $40$ cm radius is completely filled with water and its capacity is $528\ \text{dm}^3$ (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at $70$ cm below the top of water level, then horizontal range of water falling on the ground in the beginning is ______ cm.
Answer: (B) $140\sqrt{2}$
Height of vessel: $H = \dfrac{V}{\pi r^2} = \dfrac{528 \times 10^{-3}}{\frac{22}{7} \times 0.16} = 1.05$ m $= 105$ cm. The block is also $105$ cm tall.
The hole is $70$ cm below the surface, so the efflux speed is $v = \sqrt{2g(0.70)}$. Its height above the ground is $105 + (105 - 70) = 140$ cm.
Range: $x = v\sqrt{\dfrac{2y}{g}} = 2\sqrt{hy} = 2\sqrt{70 \times 140} = 140\sqrt{2}$ cm.
Solution by Sreeraj P, M.Sc Physics