A cylindrical vessel is filled with water upto the height 1 ~m from the base. A small orifice is opened at some height in the cylinder and the water level is reduced to height of orifice in 20 ~s . If the base area of the cylinder is 100 times the area of orifice, then the height of orifice from the base is (take, g=10 ~m / s ^2 )

Step-by-step solution

Height of water in vesse =1 ~m Let orifice is at a depth h from above Time taken to reduce the water level up to orifice, t= A A₀ 2 x g where, A₀= area of orifice and A= base area. Given, gathered A A₀ =100, t=20 ~s 20=100 2 x 10 x 5 = 1 5 x= 1 5 =0.2 ~m or 20 ~cm gathered Now, height of orifice from base, h=100-20=80 ~cm