Speed of Efflux

Q. A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s) through a small hole on the side wall of the cylinder near its bottom is

1. 10
2. 25.5
3. 5
4. 20

Q. if the present units of length, time and mass (m, s, kg) are changed to 100m, 100s, and 1/10 k then 1 new unit of velocity is increased 10 times 2 " force decreased 1/1000 times 3 " enegy increased 10 time

Q.

A glass flask is filled up to a mark with 50 cc of mercury at ${18}^{o}C$. If the flask and contents are heated to ${38}^{o}C$, how much mercury will be above the mark? ( for glass is $9\times {10}^{-6}/{}^{o}C$ and coefficient of real expansion of mercury is $180\times {10}^{-6}/{}^{o}C$)

1. 0.85 cc

2. 0.46 cc

3. 0.153 cc

4. 0.05 cc

Q. The pressure of the gas, filled in the bulb of a constant volume gas thermometer are 60 cm and 80 cm of mercury column at 0°C and 100°C respectively. If its bulb is immersed in a liquid at 80°C temperature. Then its pressure in mercury column will be:- (1)66 cm (2)70 cm (3)76 cm (4)78 cm

Q. a flywheel of mass 5 kg has anradius of 0.2 m . it is making 240 rpm . the average torque necessary to bring it to rest in 20 s is

Q. how much force is required to stop a bus (in 10 seconds) of mass 5000kg moving with a speed of 72km/

Q. Two water pipes P and Q having diameter 2/100 m and 4/100 m respectively with the main supply of water. the velocity of water flowing through the pipe P is

Q. 54.A block of mass m moving with velocity Vo collides with another stationary block of mass M as shown. Maximum compression in the spring is

Q. A uniform long tubeis bent into a circle of radius R and it lies in a vertical plane. Two liquids of same volume but densities ρ and δ fill half the tube. the angle θ is.

Q. if the unit of force is 1 kilonewton, the length is 1km and time is 100 second what will be the unit of mass

Q. Water flows steadily from an open tank as shown in figure. Assuming area of cross-section of the hole is much less than the area of cross-section of the tank, which of the following option(s) is/are correct? (Take value of $g=10{\text{m/s}}^2$).

1. Velocity of water coming out of the pipe is $4\sqrt{10}{\text{ms}}^{-1}$.
2. Velocity of water coming out of the pipe is $\sqrt{10}{\text{ms}}^{-1}$.
3. Value of $x$ is $7.97\text{m}$.
4. Value of $x$ is $9.97\text{m}$

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

Q. 34. A cricketer catches a ball of mass 200g in 0.2 s initially moving with speed of 30m/s he experience an average force of the magnitude of

Q. a force f=6t^2i^ +4tj^ acts on a particle of mass 3 kg. What will be the velocity of the particle at t=3 second if at t=0, the particle was at rest; 1)18i^+6J^ 2)18i^+121j^ 3)12i^ +6j^ 4)none

Q. A cylindrical vessel is filled with water upto a height of $4\text{m}$. The cross-sectional area of the orifice at the bottom is $\frac{1}{100}$ that of the vessel. Then:

1. 1.5 minutes is the required time to empty the tank.
2. Initial velocity of discharge is $8.85\text{m/s}$.
3. Velocity of discharge will decrease with time.
4. Same amount of water can be thrown out from the orifice in $45\text{seconds}$ if the level of water is maintained at $4\text{m}$.

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

Q.

A long cylindrical glass vessel has a small hole of radius 'r' at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension T) without any water entering inside is

1. 

2. 

3. 

4. 

Q. A particle of t mass m =1kg is moving in a horizontal circular path with cons†an t speed 10m/s.If it turns 60 degree in 5 s then av force acted on it is

Q. 22.The water drops fall at regular intervals from a tap 5m above the ground.The their drop is leaving the tap at instant the first drop touches the ground.Measure the height of 2nd drop at that instant

Q. A particle of mass 2g executes S.H.M. with a period of 12s and amplitude 10cm.Find the acceleration of the particle and the restoring force on the particle when itit is 2cm form its mean position.

Q. the force of a particle of mass 1kg is depend on displacement as f=4x then frequency of S.H.M is

Q. The area of two holes $A$ and $B$ are $2a$ and $a$ respectively. The holes are at depths $\frac{H}{3}$ and $\frac{2H}{3}$ from the surface of water. Find the correct option(s) -

1. The velocity of efflux at hole $B$ is $2$ times the velocity of efflux at hole $A$
2. The velocity of efflux at hole $B$ is $\sqrt{2}$ times the velocity of efflux at hole $A$
3. The discharge is same through both the holes
4. The discharge through hole $A$ is $\sqrt{2}$ times the discharge through hole $B$

Q. Water is filled in a tank up to 3m height. The base of tank is at a height 1m from ground. What should be the height of hole made in it so that water can be sprayed up to maximum horizontal distance.

Q. in a particular system the unit of length, mass and time is to be 10cm , 10g and 0.1s so the unit of force in this system will be equivalent to ?

Q. A U-tube of base length l is filled with same volume of two liquids of densities ρ and 2ρ. It is moving with an acceleration a on the horizontal plane. If the height difference between the 2 surfaces (open to the atmosphere) becomes zero; then the height of the liquids h is given by( in terms of a, g and l

Q. A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h/2 and from h/2 to zero is

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

Q. 85. water is filled in a tank up to 3 metre height. the base of the tank is at height 1 m above the ground. what should be the height of a hole made in it. so that water can be sprayed up to a maximum horizontal distance.

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. A non-uniform bar of weight $W$ is suspended at rest by two strings of negligible weight as shown in fig. The angles made by the strings with the vertical are ${36.9}^o$ and ${53.1}^o$ respectively. The bar is $2m$ long. Calculate the distance d of the center of gravity of the bar from its left end.

Q. A cylindrical tank has a hole of $1c{m}^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70c{m}^3/sec$. then the maximum height up to which water can rise in the tank is

1. 2.5 cm
2. 5 cm
3. 10 cm
4. 0.25 cm