For amongst the following curves which one shows the variation of velocity with time for a small-sized spherical body falling vertically in a long column of viscous liquids

1.  

2.  

3.  

4.  

A sphere of mass m is dropped from a tall tower when it falls by 10 m, it attains terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first 10 m is ${\mathrm{w}}_1$ and during next 10 m is ${\mathrm{w}}_2$ then

(1) ${\mathrm{w}}_1$ < ${\mathrm{w}}_2$

(2) ${\mathrm{w}}_1$ > ${\mathrm{w}}_2$

(3) ${\mathrm{w}}_1$ = ${\mathrm{w}}_2$

(4) ${\mathrm{w}}_1$ $\ge$ ${\mathrm{w}}_2$

Water is flowing from a source as shown in the figure. Let A be the cross-sectional area of the liquid flow at the time when velocity is 5 m/s. The cross-sectional area of the liquid flow when the water has descended by 10 meters is [Take g = 10 m/${\mathrm{s}}^2$]

(1) 3A

(2) $\frac{\mathrm{A}}{3}$

(3) $\frac{\mathrm{A}}{2}$

(4) 2A

Water flows through a horizontal tube of variable cross-section. The area of the cross-section at A and B are 4 ${\mathrm{mm}}^2$ and 2 ${\mathrm{mm}}^2$ respectively. If 1 cc of water enters per second through A, then the speed of the water at B is:-

1. 25 cm/s

2. 50 cm/s

3. 100 cm/s

4. 5 cm/s

Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new steady velocity will be

1. 2v

2. $\sqrt{2}$v

3. $2^{\frac{2}{3}}v$

4. $\frac{\mathrm{v}}{\sqrt{2}}$

In the given figure, the velocity ${\mathrm{v}}_3$ of inc fluid flowing through the tube will be

(1) 3 m/s

(2) 4,5 m/s

(3) 3.5 m/s

(4) 5 m/s

A lead sphere of mass \(m\) falls in a viscous liquid with terminal velocity \(v\). Another lead sphere of mass \(M\) falls through the liquid with terminal velocity \(4v\). The ratio \(\frac{M}{m}\) is:
1. \(2\)
2. \(4\)
3. \(8\)
4. \(16\)

The diameter of a syringe is \(4~\text{mm}\) and the diameter of its nozzle (opening) is \(1~\text{mm}\). The syringe is placed on the table horizontally at a height of \(1.25~\text{m}\). If the piston is moved at a speed of \(0.5~\text{m/s}\), then considering the liquid in the syringe to be ideal, the horizontal range of liquid is: \(\left(g = 10~\text{m/s}^2 \right)\)
1. \(4~\text{m}\)
2. \(8~\text{m}\)
3. \(0.4~\text{m}\)
4. \(0.2~\text{m}\)

The value of Reynold's number for which the flow of water through a pipe becomes turbulent is:

(1) 500

(2) 900

(3) 750

(4) 3000

From the given diagram, what is the velocity \(v_3?\)
               
1. \(4~\text{m/s}\)
2. \(3~\text{m/s}\)
3. \(1~\text{m/s}\)
4. \(2~\text{m/s}\)