A tank is filled up to a height `2H` with a liquid and is placed on a platform of height `H` from the ground, the distance x from the ground where a small hole is punched to get the maximum range R is
.

Options

A. `H`
B. `1.25H`
C. `1.5H`
D. `2H`

Answer

C

Explanation

As `x=1/2"gt"^(2)implies t=sqrt((2x)/r)`
velocity of efflux `v=sqrt(2g(H-x))`
Hence `R=vt=2sqrt(x(3H-x))`
For range to be maximum `(dR)/(dx)=0`
which gives `x=3/2H`
Alternatively :
Maximum range is also equal to average of two heights
`x=(H+2H)/2=(3H)/2`