In a cylindrical vessel containing liquid of density `rho` there are two holes in the side walls at heights of `h_(1)` and `h_(2)` respectively such that the range of efflux at the bottom of the vessel is same. The height of a hole for which the range of efflux would be maximum, will be

Options

A. `h_(2)-h_(1)`
B. `h_(2)+h_(1)`
C. `(h_(2)-h_(1))/(2)`
D. `(h_(2)+h_(1))/(2)`

Answer

A, B

Explanation

`x=v_(1)t_(1)=v_(2)t_(2)`
`sqrt(2g(H-h_(1)))xxsqrt((2h_(1))/(g))=sqrt(2g(H-h_(2)))xxsqrt((2h_(2))/(g))`
`h_(1)(H-h_(1))=h_(2)(H-h_(2))`
`Hh_(1)-h_(1)^(2)=Hh_(2)-h_(2)^(2)`
`H(h_(2)-h_(1))=h_(2)^(2)-h_(1|2)`
`H=(h_(2)+h_(1))`
For `x_(max),h=(H)/(2)impliesh=(h_(1)+h_(2))/(2)`