A water tank of height `H`, completely filled with water is placed on a level ground. It has two holes one at a depth `h` from top and the other at height `h` form its base. The water ejecting from

Options

A. both the holes will fall at the same spot
B. upper hole will fall farther than that form the lower hole
C. upper hole will fall closer than that form the lower hole
D. more information is required.

Answer

A

Explanation

Velocity of water coming out from hole `A`
`v_(1) = sqrt(2gh)`
Velocity of water coming out from hole B
`=v_(2)=sqrt(2g(H-h))`
Time taken by water to reach the ground from hole `A`
`=t_(1) = sqrt(2(H-h)//g)`
Time taken by water to reach the ground from hole `B`
`=t_(2) = sqrt(2h//g)`
Obviously, range on the ground for both is the same
`:. R = v_(1)t_(1) = v_(2)t_(2) = 2gsqrt(h(H-h))`.