Consider a water jar of radius R that has water filled up to height `H` and is kept on a stand of height `h` (see figure) through a hole of radius `r(rltltR)` at its bottom the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. it the radius of the cross-section of water stream when it hits the ground is x. then.

Options

A. `x=r ((H)/(H+h))`
B. `x=r ((H)/(H+h))^(1/2)`
C. `x=r ((H)/(H+h))^(1/4)`
D. `x=r ((H)/(H+h))^(2)`

Answer

C

Explanation

From equation of continuity
`A_(1)V_(1)=A_(2)V_(2)`
`pir^(2) sqrt(2gH)=pir^(2) sqrt(2g(h+H))`
`r^(2)-sqrtH/sqrt((h+H))=x^(2)`
`x=r ((H)/(h+H))^(1/4)`