A cylindrical drum of radius 20 cm has a capacity of 2.5 m^(3) of water. It contains 1.8 m^(3) of water and is placed on an iron block of same size as the drum. Calculate the horizontal range of water on the ground from an orifice made at lower end of drum, perepndicular to its length.

A cylindrical drum of radius 20 cm has a capacity of 2.5 m^(3) of wate

1.	A cylindrical drum of radius 20 cm has a capacity of 2.5 m^(3) of water. It contains 1.8 m^(3) of water and is placed on an iron block of same size as the drum. Calculate the horizontal range of water on the ground from an orifice made at lower end of drum, perepndicular to its length.
Answer» Solution :Radiu of DRUM r=20cm=0.2 m Capacity fo drum `=2.5 m^(3)` Let l be the height of the drum. THUS, `pi r^(2)l=2.5` `rArrrl=(2.5)/pi^(2)=(2.5 xx 7)/(22 xx (0.2)^(2))` =19.88 m Height of block =l=19.88m Volume of water inside the tank `=1.8 m^(3)` Let H be the height of the water column in the drum. Then, `pi r^(2) h=1.8 m^(3)` `rArr h=(1.8)/(pi r^(2))=(1.8 xx 7)/(22 xx (0.2)^(2))` =14.32 m Time taken by water to REACH the ground `t=sqrt((2h)/(g))` Also, efflux velocity, `u=sqrt(2gl)` [l=height of orifice from ground] Horizontal range of water, then R=vt `=sqrt(2gl) xx sqrt((2h)/(g)) =2sqrt(LH)` `=2sqrt(19.88 xx 14.32)=33.75m`