A tank is filled up to a height h with a liqu | vedclass

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

Question

(D) The velocity of the liquid through the orifice is given by Torricelli's law: $v = \sqrt{2gy}$.The height of the orifice from the ground is $(h - y

Vedclass · Accepted Answer

$(a)$ or $(c)$ both

Vedclass · Answer

(D) The velocity of the liquid through the orifice is given by Torricelli's law: $v = \sqrt{2gy}$.The height of the orifice from the ground is $(h - y) + h = 2h - y$. The time taken by the liquid to reach the ground is:$t = \sqrt{\frac{2(2h - y)}{g}}$.The horizontal range $x$ is given by the product of horizontal velocity and time:$x = v \cdot t = \sqrt{2gy} \cdot \sqrt{\frac{2(2h - y)}{g}} = \sqrt{4y(2h - y)}$.To find the maximum range,we maximize $x^2$ with respect to $y$:$x^2 = 4y(2h - y) = 8hy - 4y^2$.Differentiating with respect to $y$ and setting to zero:$\frac{d(x^2)}{dy} = 8h - 8y = 0 \implies y = h$.Substituting $y = h$ back into the expression for $x$:$x_m = \sqrt{4h(2h - h)} = \sqrt{4h^2} = 2h$.Since both $y = h$ and $x_m = 2h$ are correct,the correct option is $(d)$.

$A$ tank is filled up to a height $h$ with a liquid and is placed on a platform of height $h$ from the ground. To get the maximum range $x_m$,a small hole is punched at a distance of $y$ from the free surface of the liquid. Then:

Similar Questions

$A$ vessel completely filled with water has two holes $P$ and $Q$ at depths $2h$ and $8h$ from the top,respectively. Hole $P$ is a square of side $a$ and hole $Q$ is a circle of radius $r$. If the volume of water flowing out per second from both holes is the same,then the side $a$ of hole $P$ is:

$A$ cylindrical vessel of $90 \ cm$ height is kept filled up to the brim. It has four holes $1, 2, 3, 4$ which are respectively at heights of $20 \ cm, 30 \ cm, 45 \ cm,$ and $50 \ cm$ from the horizontal floor $PQ.$ The water falling at the maximum horizontal distance from the vessel comes from:

$A$ vessel is filled with water up to a height $h$. When a hole is made at the bottom,all the water drains out in time $t$. If the vessel is filled with water up to a height $4h$,how long will it take for the water to drain out completely when a hole is made at the bottom?

$A$ 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

Vedclass Test Series

Exam Paper Generator

Online Exam Module