A cylinder of height h is filled with water a | vedclass

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

Question

(B) Let $y$ be the depth of a hole below the water surface. The velocity of efflux is $v = \sqrt{2gy}$.The height of the hole from the ground is $H_{h

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Let $y$ be the depth of a hole below the water surface. The velocity of efflux is $v = \sqrt{2gy}$.The height of the hole from the ground is $H_{hole} = h - y + h/2 = \frac{3h}{2} - y$.The time taken for water to reach the plane $PQ$ is $t = \sqrt{\frac{2 H_{hole}}{g}} = \sqrt{\frac{2(3h/2 - y)}{g}} = \sqrt{\frac{3h - 2y}{g}}$.The horizontal range $x$ is given by $x = v \cdot t = \sqrt{2gy} \cdot \sqrt{\frac{3h - 2y}{g}} = \sqrt{2y(3h - 2y)} = \sqrt{6hy - 4y^2}$.To maximize $x$,we differentiate with respect to $y$ and set it to zero: $\frac{dx}{dy} = \frac{1}{2\sqrt{6hy - 4y^2}} \cdot (6h - 8y) = 0$.This gives $6h - 8y = 0$,or $y = \frac{3h}{4}$.The depth $y$ is measured from the top. The heights of the holes from the base are $0, h/4, h/2, 3h/4$. Thus,the depths $y$ from the top are $h, 3h/4, h/2, h/4$ for holes $1, 2, 3, 4$ respectively.The range is maximum when $y = 3h/4$,which corresponds to hole number $2$.

Similar Questions

Which of the following oxides is strongly basic?

Which of the following substances is the least soluble in water?

$A$ variable circle passes through the fixed point $A(p, q)$ and touches the $x$-axis. The locus of the other end of the diameter through $A$ is

$A$ man is watching two trains,one leaving and the other coming with equal speed of $4\,m/s$. If they sound their whistles each of frequency $240\,Hz$,the number of beats per second heard by the man will be equal to (velocity of sound in air $= 320\,m/s$)

In a permanent magnet at room temperature,

Vedclass Test Series

Exam Paper Generator

Online Exam Module