A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 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.

Step-by-step solution

Volume of the cylindrical vessel, V = 528 dm ^3 = 528000 cm ^3 Radius of the vessel, r = 40 cm Let the height of the vessel be H . V = r^2 H 528000 = 22 7 (40)^2 H H = 528000 7 22 1600 = 105 cm The vessel is placed on a block of height equal to the vessel, so the height of the block is 105 cm. Depth of the hole from the top water level, h = 70 cm Height of the hole from the ground, y = Height of block + (H - h) y = 105 + (105 - 70) = 140 cm Velocity of efflux, v = 2gh Time of flight of water, t = 2y g Horizontal ra