Q.

A water barrel stands on a table of height h. If a small hole 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?

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a

R2h

b

R22h

c

R24h

d

4R2h

answer is C.

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Detailed Solution

From Torricelli's theoremv = 2gd  ------(i)where y is horizontal velocity and d is the depth of water in barrel.Time t to hit the ground is given byh = 12gt2    or t = 2hg∴  R = vt = (2gd)2hg = 2dh    (Using (i))∴ R2 = 4dh or d = R24h
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