Two pieces of metal when immersed in a liquid have equal upthrust on them; then

(1) Both pieces must have equal weights

(2) Both pieces must have equal densities

(3) Both pieces must have equal volumes

(4) Both are floating to the same depth

A candle of diameter \(d\) is floating on a liquid in a cylindrical container of diameter \(D(D>>d)\) as shown in the figure. If it is burning at the rate of \(2~\text{cm/hour}\) then the top of the candle will:
            

Construction of submarines is based on 
(1) Archimedes’ principle               

(2) Bernoulli’s theorem

(3) Pascal’s law                             

(4) Newton’s laws

In which one of the following cases will the liquid flow in a pipe be most streamlined  ?

(1) Liquid of high viscosity and high density flowing through a pipe of small radius

(2) Liquid of high viscosity and low density flowing through a pipe of small radius

(3) Liquid of low viscosity and low density flowing through a pipe of large radius

(4) Liquid of low viscosity and high density flowing through a pipe of large radius

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is -

(1) 4 times that in the other pipe

(2) 3 times that in the other pipe

(3) 2 times that in the other pipe

(4) 6 times that in the other pipe

An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is

(1)    3.0 m/s                          

(2) 1.5 m/s                     

(3) 1.0 m/s                             

(4) 2.25 m/s

The velocity of kerosene oil in a horizontal pipe is \(5 ~\text{m/s}.\) If \(g = 10 ~\text{m/s} ^2 ,\) then the velocity head of oil will be:
1. \(1.25 ~\text m\)
2. \(12.5 ~\text m\)
3. \(0.125 ~\text m\)       
4. \(125 ~\text m\)

In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the

(a) Height of the liquid in the tube A is maximum

(b) Height of the liquid in the tubes A and B is the same

(c) Height of the liquid in all the three tubes is the same

(d) Height of the liquid in the tubes A and C is the same

A manometer connected to a closed tap reads $3.5\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$. When the valve is opened, the reading of manometer falls to $3.0\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$ , then velocity of flow of water is
(1) 100 m/s                                       

(2) 10 m/s

(3) 1 m/s                                           

(4) $10\sqrt{10}$ m/s

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) 20

(3) 25.5                                     

(4) 5