A square gate of size 1,m times 1,m is hinged | vedclass

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

Question

(c)

The net force acting on the gate element of width dy at a depth $y$ from the surface of the fluid, is

$dy  =\left( p _0+\rho_{ g } y -

Vedclass · Accepted Answer

$\frac{\rho g }{6}$

Vedclass · Answer

(c)

The net force acting on the gate element of width dy at a depth $y$ from the surface of the fluid, is

$dy  =\left( p _0+ho_{ g } y - p _0ight) 	imes 1 dy$

$=ho 	ext { gydy }$

Torque about the hinge is

$d 	au=\operatorname{pgydy} 	imes\left(\frac{1}{2}- y ight)$

Net torque experienced by the gate is

$	au_{	ext {net }}=\int d 	au+ F 	imes \frac{1}{2}=0$

$\Rightarrow F =\frac{ho g }{6}$

A square gate of size $1\,m \times 1\,m$ is hinged at its mid-point. A fluid of density $\rho$ fills the space to the left of the gate. The force F required to hold the gate stationary is

Similar Questions

A cylinder stands vertical in two immiscible liquids of densities $\rho$ and $2 \rho$. The height of two liquids are shown. Find the difference in pressure at point $A$ and $B$

The diagram shows a simple mercury barometer.Which of the following does not cause the height of the mercury column to vary ?

The volume of an air bubble is doubled as it rises from the bottom of lake to its surface. The atmospheric pressure is $75 \,cm$ of mercury. The ratio of density of mercury to that of lake water is $\frac{40}{3}$. The depth of the lake in metre is .........

From the adjacent figure, the correct observation is

A wooden block floats in a liquid with $40\%$ of its volume inside the liquid. When the vessel containing he liquid starts rising upwards with acceleration $a = g/2$, the percentage of volume inside the liquid is ......... $\%$