In a cylindrical vessel containing liquid of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The range of efflux $x$ for a hole at height $h$ from the bottom in a vessel filled with liquid to a total height $H$ is given by $x = 2 \sqrt{(H

Vedclass · Accepted Answer

$\frac{h_2 + h_1}{2}$

Vedclass · Answer

(D) The range of efflux $x$ for a hole at height $h$ from the bottom in a vessel filled with liquid to a total height $H$ is given by $x = 2 \sqrt{(H - h)h}$.Given that the range of efflux is the same for two holes at heights $h_1$ and $h_2$,we have:$2 \sqrt{(H - h_1)h_1} = 2 \sqrt{(H - h_2)h_2}$$(H - h_1)h_1 = (H - h_2)h_2$$Hh_1 - h_1^2 = Hh_2 - h_2^2$$H(h_1 - h_2) = h_1^2 - h_2^2$$H(h_1 - h_2) = (h_1 - h_2)(h_1 + h_2)$$H = h_1 + h_2$The range of efflux $x = 2 \sqrt{Hh - h^2}$ is maximum when the term inside the square root is maximum. Let $f(h) = Hh - h^2$. For maximum,$f'(h) = 0$.$H - 2h = 0 \Rightarrow h = \frac{H}{2}$.Substituting $H = h_1 + h_2$,we get the height for maximum range as $h = \frac{h_1 + h_2}{2}$.

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 the same. The height of a hole,for which the range of efflux would be maximum,is:

Similar Questions

$A$ rectangular vessel,when full of water,takes $10 \text{ minutes}$ to be emptied through an orifice in its bottom. How many minutes will it take to be emptied when half-filled with water?

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to zero is

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to $0$ is

If in a stationary lift,a man is standing with a bucket full of water,having a hole at its bottom. The rate of flow of water through this hole is $R_0$. If the lift starts to move up and down with the same acceleration $a$,and the rates of flow of water are $R_u$ and $R_d$ respectively,then:

There is a hole at the bottom of a water tank. The total pressure at the bottom is $3 \, atm$ $(1 \, atm = 10^{5} \, N/m^{2})$. What is the velocity of the water coming out of the hole?

Vedclass Test Series

Exam Paper Generator

Online Exam Module