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A water barrel stands on a table of heig...

A water barrel stands on a table of height `h`. If a small holes is punched in the side of the barrel at its base, it is found that the resultant stream of water strikes the ground at a horizontal distance `R` from the table. What is the depth of water in the barrel?

A

`(R^(2))/(h)`

B

`(R^(2))/(2h)`

C

`(R^(2))/(4h)`

D

`(4R^(2))/(h)`

Text Solution

Verified by Experts

The correct Answer is:
C
From Torricelli's theorem
`v=sqrt(2gd)" "…(i)`
where v is horizontal velocity and d is the depth of water in barrel.
Time t to hit the ground is given by
`h=(1)/(2)"gt"^(2)` or `t=sqrt((2h)/(g))`
`therefore R=vt=sqrt((2gd))sqrt((2h)/(g))=2sqrt(dh)" "` (Using (i))
`R^(2)=4dh` or `d=(R^(2))/(4h)`
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