Speed of Efflux

Q.

iIf the unit of force is kN , the length is 1 km and time 100s , then what will be the unit of mass ?

Q.

What is kgf unit and how can we calculate it?

Q. A cylindrical vessel contains a liquid of density $\rho$ up to a height $H$. The liquid is closed by a piston of mass $m$ and area of cross-section $A$. There is a small hole at the bottom of the vessel. The speed $v$ with which the liquid comes out of the hole is

1. $\sqrt{3(gH+\frac{mg}{\rho A})}$
2. $\sqrt{2(gH+\frac{mg}{\rho A})}$
3. $\sqrt{5(gH+\frac{mg}{\rho A})}$
4. $\sqrt{6(gH+\frac{mg}{\rho A})}$

Q. A tank is filled with water upto a height $H$. Water is allowed to come out of a hole $P$ in one of the walls at a depth $h$ below the surface of water (see figure). Express the horizontal distance $X$ in terms of $H$ and $h$.

1. $X=\sqrt{h(H-h)}$
2. $x=\sqrt{\frac{h}{2}(H-h)}$
3. $X=4\sqrt{h(H-h)}$
4. $X=2\sqrt{h(H-h)}$

Q. A rectangular vessel when full of water, takes $10\text{min}$ to be emptied through an orifice at its bottom. How much time will it take to be emptied when it is half filled ?

1. $9\text{min}$
2. $7\text{min}$
3. $3\text{min}$
4. $5\text{min}$

Q.

Can a body have zero velocity and still be accelerating?

Q. There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is $h$. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to -

1. $h^{1/2}$
2. $h$
3. $h^{3/2}$
4. $h^2$

Q. A hole is made at the bottom of the tank filled with water (density $1000{\text{kg/m}}^3$). If the total pressure at the bottom of the tank is 3 atmosphere (1 atmosphere = ${10}^5{\text{N/m}}^2$), then the velocity of efflux is

1. $\sqrt{200}\text{m/s}$
2. $\sqrt{400}\text{m/s}$
3. $\sqrt{500}\text{m/s}$
4. $\sqrt{800}\text{m/s}$

Q. A large tank is filled with water to a height $H$. A small hole is made at the base of the tank. It takes $T_1$ time to decrease the height of water to $\frac{H}{\eta }(\eta >1),$ and it takes $T_2$ time to take out the rest of the water. If $T_1=T_2,$ then the value of $\eta$ is

1. $2$
2. $4$
3. $3$
4. $5$

Q. A large container with open top and uniform cross-sectional area $\left(A\right)$ has a small hole of cross-sectional area $a$ in its side wall near the bottom. The container is kept on a smooth horizontal platform and contains a liquid of density $\rho$ and mass $m$. If the liquid starts flowing out of the hole at time $t=0$, the initial acceleration $\left(\alpha \right)$ of the container is

1. $\frac{ga}{A}$
2. $\frac{gA}{a}$
3. $\frac{2ga}{A}$
4. $\frac{gA}{2a}$
   

Q. A large tank is filled with water $(\text{density}={10}^3{\text{kg/m}}^3).$ A small hole is made at a depth of $10\text{m}$ below water surface. The range of water coming out of the hole is $R$ on the ground. What extra pressure must be applied on the water surface so that the range become $2R$ ?
$(p_0=1\text{atm}={10}^5\text{Pa}$ and $g=10{\text{m/s}}^2)$

1. $1\text{atm}$
2. $2\text{atm}$
3. $4\text{atm}$
4. $3\text{atm}$

Q.

Water flows through a horizontal tube of variable cross section figure. The area of cross section at A and B are 4 $m{m}^2$ and 2$m{m}^2$ respectively. If 1 cc of water enters per second through A, find (a) the speed of water at A, (b) the speed of water at B and (c) the pressure difference $P_A—P_B$.

Q. A square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4h$ from the surface of water in a water tank kept on a horizontal surface. If $l<<h$, $r<<h$ and the rate of water flow from the holes is the same, then $r$ is equal to -

1. $\frac{l}{\sqrt{2\pi }}$
2. $\frac{l}{\sqrt{3\pi }}$
3. $\frac{l}{3\pi }$
4. $\frac{l}{2\pi }$

Q.

A liquid of density $\rho$ is coming out of a hose pipe of radius a with horizontal speed$v$and hits a mesh.$50\%$ of the liquid passes through the mesh unaffected. $25\%$ looses all of its momentum and$25\%$ comes back with the same speed. The resultant pressure on the mesh will be:

1. $\rho v^2$

2. $\left(3/4\right)\rho v^2$

3. $\left(1/2\right)\rho v^2$

4. $\left(1/4\right)\rho v^2$

Q. The velocity of efflux of a liquid for a small height of water column in a tank, through an orifice at the bottom of the tank does not depend on:

1. density of liquid
2. none of the above
3. height of the liquid column above the orifice
4. acceleration due to gravity

Q. A cylindrical vessel is filled with a liquid up to a height $H$. A small hole is made in the vessel at a distance $y$ below the liquid surface as shown in figure. The liquid emerging from the hole strikes the ground at distance $X$.

1. $X$ remains same if the hole is at depth $y$ or $H-y$.
2. $X$ is maximum for $y=\frac{H}{2}$.
3. both (a) and (b) are correct.
4. both (a) and (b) are wrong.

Q.

A cube of ice is floating in water contained in a vessel. When the ice melts, the level of water in the vessel

1. rises

2. falls

3. remains unchanged

4. falls at first and then rises to the same height as before.

Q. A water tank standing on the floor has two small holes punched in the vertical wall, one above the other. The holes are $2.4\text{cm}$ and $7.6\text{cm}$ above the floor. If the jets of water from the holes hit the floor at the same point, then the height of water in the tank is

1. $10\text{cm}$
2. $5\text{cm}$
3. $20\text{cm}$
4. $4.8\text{cm}$

Q. If the velocity head of a stream of water is equal to $10\text{cm}$, then its speed of flow is approximately

1. $1.4\text{m/s}$
2. $1.7\text{m/s}$
3. $1.8\text{m/s}$
4. $1.2\text{m/s}$

Q. A cylindrical container of radius ${}^{\prime }{R}^{\prime }$ and height ${}^{\prime }{h}^{\prime }$ is completely filled with a liquid. Two horizontal L – shaped pipes of small cross-sectional area ${}^{\prime }{a}^{\prime }$ are connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions. Then the torque due to ejected liquid on the system is

1. $4agh\rho R$
2. $8agh\rho R$
3. $2agh\rho R$
4. None of these

Q. In a resonance column experiment, a tuning fork of frequency $400\text{Hz}$ is used. The first resonance is observed when the air column has a length $20.0\text{cm}$ and the second resonance is observed when the air column has a length of $62.0\text{cm}$. Find the distance above the open end where the pressure node is formed ?

1. $1\text{cm}$
2. $2\text{cm}$
3. $1.5\text{cm}$
4. $3\text{cm}$

Q. The level of water in a tank is $5\text{m}$ high. A hole of area $1{\text{cm}}^2$ is made at the bottom of the tank. The rate of leakage of water from the hole is : [Take $g=10{\text{m/s}}^2$]

1. ${10}^{-2}\text{m}{}^3\text{/s}$
2. ${10}^{-3}\text{m}{}^3\text{/s}$
3. ${10}^{-4}\text{m}{}^3\text{/s}$
4. ${10}^{-1}\text{m}{}^3\text{/s}$

Q. A tank is filled upto height $h$ with a liquid and is placed on a platform of height $h$ from the ground. To get maximum range $x_m$, a small hole is punched at a distance $y$ from the free surface of the liquid. Then find the value of maximum range ($x_m$).

1. $x_m=h$
2. $x_m=2h$
3. $x_m=4h$
4. $x_m=\frac{h}{2}$

Q. Water $(\rho =1000{\text{kg/m}}^3)$ and kerosene $(\rho =800{\text{kg/m}}^3)$ are filled separately in two identical cylindrical vessels having small heights. Both vessels have small holes at their bottom. The speed of the water and kerosene coming out of their holes are $v_1$ and $v_2$ respectively. Select the correct option.

1. $v_1=v_2$
2. $v_1=3v_2$
3. $v_1=2v_2$
4. $v_1=4v_2$

Q. Water is filled in a tank upto $3\text{m}$ height. The base of the tank is at height $1\text{m}$ above the ground. What should be the height of a hole made in it, so that water can be sprayed upto maximum horizontal distance on the ground?

1. $3\text{m}$ from ground
2. $1.5\text{m}$ from ground
3. $2\text{m}$ from ground
4. $2.5\text{m}$ from ground

Q. A tank is filled upto a height $H$. The horizontal range of water coming out of the hole which is at depth $\frac{H}{4}$ from the surface level of water is

1. $\sqrt{3}H$
2. $\frac{3H}{4}$
3. $\frac{\sqrt{3}H}{2}$
4. $\frac{2H}{\sqrt{3}}$

Q. A water tank stands on the roof of a building as shown in the figure. The value of height of water above the hole $\left(h\right)$ for which the horizontal distance covered by the water $\left(x\right)$ is maximum -

1. $0.2\text{m}$
2. $0.5\text{m}$
3. $0.8\text{m}$
4. $1\text{m}$

Q.

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500m/ s with respect to the car . The number of bullets fired per second is ten. The average thrust on the system is ??

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

1. $1:2$
2. $1:1$
3. $2:1$
4. $3:2$

Q.

The lightest liquid metal is

1. $\mathrm{Hg}$

2. $\mathrm{Na}$

3. $\mathrm{Cs}$

4. $\mathrm{Fr}$