A cylindrical vessel of height 50 ,cm is fill | vedclass

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

Question

(C) Given, the height of the cylinder is $H = 50 \,cm$.Let the hole be at a height $h$ from the bottom. The height of the water column above the hole

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(C) Given, the height of the cylinder is $H = 50 \,cm$.Let the hole be at a height $h$ from the bottom. The height of the water column above the hole is $(H - h)$.The velocity of efflux is $v = \sqrt{2g(H - h)}$.The time taken for the water to reach the table is $t = \sqrt{\frac{2h}{g}}$.The horizontal range $x$ is given by $x = v \cdot t = \sqrt{2g(H - h)} \cdot \sqrt{\frac{2h}{g}} = 2\sqrt{h(H - h)}$.To find the maximum range $x_{\max }$, we differentiate $x$ with respect to $h$ and set it to zero:$\frac{dx}{dh} = 2 \cdot \frac{1}{2\sqrt{h(H - h)}} \cdot (H - 2h) = 0$.This gives $H - 2h = 0$, or $h = \frac{H}{2}$.Substituting $h = \frac{H}{2}$ into the expression for $x$:$x_{\max } = 2\sqrt{\frac{H}{2}(H - \frac{H}{2})} = 2\sqrt{\frac{H}{2} \cdot \frac{H}{2}} = H$.Given $H = 50 \,cm$, therefore $x_{\max } = 50 \,cm$.

Similar Questions

There is a hole in the bottom of a tank containing water. If the total pressure at the bottom is $3 \text{ atm}$ $(1 \text{ atm} = 10^5 \text{ N/m}^2)$,then the velocity of water flowing from the hole is:

$A$ vessel completely filled with water has holes $A$ and $B$ at depths $h$ and $3h$ from the top respectively. The hole $A$ is a square of side $L$ and $B$ is a circle of radius $r$. The water flowing out per second from both the holes is same. Then $L$ is equal to

$A$ 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

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?

$A$ tank is filled with water and two holes $A$ and $B$ are made in it. For getting the same range,the ratio of $h^{\prime}$ to $h$ is ..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module