In a cylindrical vessel containing a liquid of density ρ , there are two holes in the side walls at heights of h1 and h2 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

Question

In a cylindrical vessel containing a liquid of density ρ , there are two holes in the side walls at heights of h1 and h2 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 <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-c7s1yobqzg7x4mvo.jpg" /> (A) h2-h1 (B) h2+h1 (C) (h2 - h1/2) (D) (h2 + h1/2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-c7s1yobqzg7xacgb.jpg" /> If H is the height of the liquid surface then for same range h2=H-h1 and for maximum range h=(H/2)=(h1 + h2/2)

Q. In a cylindrical vessel containing a liquid of density $ρ$ , 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

$h_{2} - h_{1}$

$h_{2} + h_{1}$

$\frac{h _{2} - h _{1}}{2}$

$\frac{h _{2} + h _{1}}{2}$

If $H$ is the height of the liquid surface then for same range
$h_{2} = H - h_{1}$
and for maximum range
$h = \frac{H}{2} = \frac{h _{1} + h _{2}}{2}$

Q. In a cylindrical vessel containing a liquid of density ρ , there are two holes in the side walls at heights of h1​ and h2​ 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

h2​−h1​

h2​+h1​

2h2​−h1​​

2h2​+h1​​