Untitled Document

Question Bank No: 1

1. A tank containing water has an orifice on one vertical side. If the centre of the orifice is 4.9 m below the surface level in the tank, the velocity of discharge is

a)		4.9 ${ms}^{- 1}$
b)		9.8 ${ms}^{- 1}$
c)		2.45 ${ms}^{- 1}$
d)		zero

2. A metal plate of area 500 ${cm}^{2}$ is kept on a horizontal surface with a layer of castor oil of thickness 0.5 mm between them. The horizontal force required to drag the plate with a velocity of 2 cm/s is ( $η$ = 0.9 $kg m^{- 1} s^{- 1}$ )

a)		18 N
b)		1.8 N
c)		180 N
d)		0.018 N

3. A ball rises to the surface at a constant velocity in a liquid whose density is 4 times that of the material of the ball. The ratio of the force of friction acting on the rising ball and its weight is

a)		3 : 1
b)		1 : 3
c)		4 : 1
d)		1 : 4

4. The terminal velocity of a rain drop of radius 'r' falling down through the atmosphere is $[η = coeff . of viscosity of air, d_{0} = density of air, d density of water]$

a)		$\frac{2 r^{2} (d - d_{0}) g}{9 η}$
b)		$\frac{2 r^{2} (d + d_{0}) g}{9 η}$
c)		$\frac{2 r^{2} (d - d_{0}) g}{η}$
d)		$\frac{2 r^{2} (d + d_{0}) g}{η}$

5. The pressure energy per unit volume of fluid is (P is the pressure and d is the density)

a)		P/d
b)		P
c)		Pd
d)		d/P

6. If $V_{1}$ and $V_{2}$ be the volumes of liquids flowing out of the same tube in the same interval of time and $y_{1}$ and $y_{2}$ their coefficients of viscosity respectively then

a)		$y_{1} / y_{2} = V_{2} / V_{1}$
b)		$y_{1} / y_{2} =$ $V_{1} / V_{2}$
c)		$y_{1} / y_{2} = {V_{1}}^{2} / {V_{2}}^{2}$
d)		$y_{1} / y_{2} = {V_{2}}^{2} / {V_{1}}^{2}$

7. A good lubricant should have

a)		high viscosity
b)		low viscosity
c)		moderate viscosity
d)		high density

8. A capillary of length l, radius r is connected in series with another tube of length l/3 and radius r/2. A liquid is made to flow through the system. If the pressure across the first capillary is $ρ$ , then the pressure across the second capillary is

a)		16p/3
b)		4p/3
c)		p
d)		3p/16

9. The water level in a cylinder is H. Water is allowed to come out of a hole P at a depth h below the surface of water. The horizontal range R is
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a)		$\sqrt{h (H - h)}$
b)		$2 \sqrt{h (H - h)}$
c)		$\sqrt{2 gh (H - h)}$
d)		$\sqrt{\frac{h}{2} (H - h)}$

10. The height of water in a cylinder is H. The water coming out of two pin holes P and Q have the same range. If the hole Q is at a height h above the ground, then the height of P above the ground is
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a)		2h
b)		H/h
c)		H - h
d)		H/2

11. Water flows through a hose of internal diameter 2 cm at a speed 1 ${ms}^{- 1}$ . The diameter of a nozzle to get water at a speed 4 ${ms}^{- 1}$ is

a)		4 cm
b)		2 cm
c)		0.5 cm
d)		1 cm

12. Eight identical rain drops each falling with a terminal velocity 5 units coalesce to form a bigger drop. The terminal velocity of the bigger drop is

a)		5
b)		40
c)		20
d)		10

13. The masses of rain drops falling vertically from a large height are in the ratio 1 : 4. The ratio of their terminal velocities is

a)		1/4
b)		4
c)		${[1 / 4]}^{2 / 3}$
d)		${[1 / 4]}^{3 / 2}$

14. Two identical spheres of the same material fall through two liquids of coefficients of viscosity 0.001 and 0.05 units. Ratio of their terminal velocities is

a)		50 : 1
b)		1 : 50
c)		1 : 5
d)		5 : 1

15. If y is the coefficient of viscosity of a liquid, K the Reynold's number, $ρ$ the density of the liquid and r the radius of a tube, the critical velocity of the liquid flowing through the tube is

a)		$K ρ / yr$
b)		$Ky / ρ r$
c)		$Kr / y ρ$
d)		$Ky / 2 ρ r$

16. A garden sprinkler has 150 small holes each of 2 ${mm}^{2}$ area. If water is supplied at the rate of $3 \times 10^{- 3} m^{3} s^{- 1}$ , the average velocity of the spray is

a)		100 ${ms}^{- 1}$
b)		0.1 ${ms}^{- 1}$
c)		10 ${ms}^{- 1}$
d)		3 ${ms}^{- 1}$

17. A capillary tube stands with its lower end dipped in a liquid for which the angle of contact is $90^{\circ}$ . The liquid

a)		will neither rise nor will its level be depressed inside the tube
b)		will be depressed inside the tube
c)		will rise inside the tube
d)		will rise upto the top of the tube

18. The two limbs of a U tube have radii r and 2r. Some water has been poured in the U tube. Surface tension of water is T. The difference of levels of water in the two tubes is

a)		zero
b)		$\frac{2 T}{r}$
c)		$\frac{T}{r}$
d)		$\frac{T}{2 r}$

19. Liquid reaches an equilibrium as shown, in a tube of internal radius r. If the surface tension of the liquid is S, the angle of contact $θ$ and the density of liquid is $ρ$ , then the pressure difference between P and Q is
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a)		$\frac{2 S \cos θ}{r}$
b)		$\frac{S}{r \cos θ}$
c)		$\frac{2 S}{r \cos θ}$
d)		$\frac{4 S \cos θ}{r}$

20. Two parallel glass plates are dipped perpendicularly in a liquid of density $ρ$ . The seperation between the plates is d and surface tension of the liquid is S. The angle of contact for glass is $θ$ . The capillary rise of liquid between the plates is

a)		$\frac{S \cos θ}{ρ d}$
b)		$\frac{2 S \cos θ}{ρ g d}$
c)		$\frac{2 S}{ρ g d \cos θ}$
d)		$\frac{S \cos θ}{ρ g d}$

21. A soap film of surface tension $30 \times 10^{- 3} {Nm}^{- 1}$ is formed on a rectangular frame. It can just support a straw PQ as shown in the figure: If g = $10 {ms}^{- 2}$ , the mass of the straw is
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a)		0.3g
b)		0.03g
c)		3g
d)		0.6 g

22. A liquid drop of diameter d breaks into 27 tiny droplets. The surface tension of the liquid is S. The change in energy is

a)		$\frac{5}{9} π d^{2} S$
b)		$2 π d^{2} S$
c)		$4 π d^{2} S$
d)		$11 π d^{2} S$

23. The radius of a soap bubble increases from $r_{1}$ to $r_{2}$ . The work done is (surface tension S)

a)		$2 \times 4 π ({r_{2}}^{2} - {r_{1}}^{2}) S$
b)		$4 π ({r_{2}}^{2} - {r_{1}}^{2}) S$
c)		$2 \times \frac{4}{3} π ({r_{2}}^{3} - {r_{1}}^{3}) S$
d)		$\frac{4}{3} π ({3 r}_{2}^{3} - {r_{1}}^{3}) S$

24. The energy spent in blowing a soap bubble of radius r is (surface tension S)

a)		$s \times 4 π r^{2}$
b)		$2 \times S \times 4 π r^{2}$
c)		$(4 / 3) π r^{3} S$
d)		$2 \times S \times 4 π r^{3}$

25. A thin layer of water is pressed between two glass plates so that it spreads over an area A. If d is the distance between the plates and S the surface tension, the normal force required to separate the plates is

a)		AS/d
b)		2SA/d
c)		Ad/S
d)		S/Ad

26. Two spherical bubbles of radii $r_{1}$ and $r_{2}$ in vaccum coalesce under isothermal conditions. The resulting bubble has a radius R. Then,

a)		$R = r_{1} + r_{2}$
b)		$R^{2} = {r_{1}}^{2} + {r_{2}}^{2}$
c)		$\frac{1}{R} = \frac{1}{r_{1}} + \frac{1}{r_{2}}$
d)		$R = \frac{r_{1} + r_{2}}{2}$

27. A capillary tube of radius 0.3mm is dipped in water. Water rises to a height of 5cm. Assuming angle of contact to be zero, the surface tension of water is

a)		0.03 ${Nm}^{- 1}$
b)		0.0735 ${Nm}^{- 1}$
c)		0.0757 ${Nm}^{- 1}$
d)		0.8 ${Nm}^{- 1}$

28. A drop of radius 0.01 mm is sprayed into 1000 droplets of equal size. The work done during the process (S is the surface tension) is

a)		$0.36 π S \times 10^{- 9} J$
b)		$3.6 π S$ $\times 10^{- 9} J$
c)		$36 π S$ $\times 10^{- 9} J$
d)		$10^{- 10} J$

29. Two soap bubbles each of radius r coalesce in vaccum under isothermal conditions to form a bigger bubble of radius R. Then R is

a)		2r
b)		$2^{1 / 2} r$
c)		$2^{1 / 3} r$
d)		$2^{3 / 2} r$

30. The energy needed to break a drop of radius R into n equal drops each of radius r is (S is the surface tension)

a)		$\frac{4}{3} π^{2} - \frac{4}{3} π R^{2}$
b)		$(4 π R^{2} - 4 π r^{2}) S$
c)		$4 π R^{2} (n^{\frac{1}{3}} - 1) S$
d)		$(4 π r^{2} - n 4 π R^{2}) S$

31. A soap bubble has a radius r and surface tension is S. The energy needed to double the diameter without change of temperature is

a)		$4 π r^{2} S$
b)		$8 π r^{2} S$
c)		$24 π r^{2} S$
d)		$12 π r^{2} S$

32. Water rises to a height of 3mm in a capillary tube of radius 0.05 cm. When the tube of radius 0.025 cm is dipped, the rise will be

a)		5mm
b)		0.15 mm
c)		6 mm
d)		7.5 mm

33. The excess of pressure inside a soap bubble is three times that inside another one. The ratio of the volumes of the two bubbles is

a)		1 : 3
b)		1 : 9
c)		27 : 1
d)		2 : 27

34. An air bubbleis under water at depth h. Pressure inside the bubble will be (surface tension = T, density of liquid = d and atmospheric pressure =P)

a)		P + d gh +2T/r
b)		P + d gh +4T/r
c)		P + d gh -4T/r
d)		P + d gh - 2T/r

35. A liquid of surface tension $72 \times 10^{- 3} {Nm}^{- 1}$ forms a bubble of radius 0.01 m. The excess pressure inside the bubble is

a)		28.8 ${Nm}^{- 2}$
b)		14.4 ${Nm}^{- 2}$
c)		144 ${Nm}^{- 2}$
d)		14.4 $dynes / {cm}^{2}$

36. A vessel whose bottom has a round hole with diameter 0.1mm is filled with water. The maximum height upto which the water can be filled with out leakage is (S. T. of water = $75 \times 10^{- 3} N m^{- 1}$ , g = ${10 ms}^{- 2}$ )

a)		1 m
b)		0.75 m
c)		0.30 m
d)		0.50 m

37. Due to capillary action, a liquid will rise in capillary tube if the angle of contact is

a)		obtuse
b)		acute
c)		zero
d)		$90^{\circ}$

38. A spring balance reads 10 kg when a bucket of water is suspended from it. What is the reading of the spring balance when an iron piece of mass 7.8 kg suspended by another string is immeresed in water? Density of iron = $7.8 \times 10^{3} kg m^{- 3}$

a)		11 kg
b)		9 kg
c)		10 kg
d)		12 kg

39. A uniform rod of length L and cross -sectional area 'a' floats vertically in a liquid of density $ρ$ . If d is the density of the rod, the length of the part of the rod immersed in the liquid is

a)		$\frac{Ld}{ρ}$
b)		$\frac{ρ \times L}{d}$
c)		$\frac{ρ}{Ld}$
d)		$\frac{d a}{ρ L}$

40. A balloon weighing 100 kg has a capacity of 1,000 $m^{3}$ . If it is filled with hydrogen, how great a pay load in kg can it support? At sea level, the density of hydrogen is 0.09 ${kgm}^{- 3}$ and that of air 1.3 ${kgm}^{- 3}$

a)		1,310 kg
b)		1,110 kg
c)		1,210 kg
d)		1,410 kg

41. A solid body X floats in water with half of it immersed. Another solid body Y floats in a liquid of relative density 1.5 with 2/3 of it immersed. The ratio of the density of the materials of X and Y is

a)		2 : 3
b)		1 : 2
c)		3 : 2
d)		1 : 3

42. The density of ice is $x$ ${kgm}^{3}$ and that of water is $y {kgm}^{- 3}$ . The change in volume when m kg of ice melts is (in $m^{3}$ )

a)		$m (y - x)$
b)		$\frac{(y - x)}{m}$
c)		$m (\frac{1}{x} - \frac{1}{y})$
d)		$(\frac{xy}{x - y})$

43. A silver ornament is suspected to be hollow. Its weight is 210g in air and 188g in water. If the relative density of silver is 10.5, the volume of the cavity is

a)		2 ${cm}^{3}$
b)		20 ${cm}^{3}$
c)		22 ${cm}^{3}$
d)		10.5 ${cm}^{3}$

44. Of the following who has won the both the Nobel Prizes for the Chemistry and Nobel Peace prize?

a)		Enrico Fermi
b)		Wallard.F.Libby
c)		Utto Hahn
d)		Linus Pauling

45. Water rises in a capillary tube to a height h. It will rise to a height more than h

a)		on the surface of sun
b)		in a lift moving down with an acceleration
c)		at the poles
d)		in a lift moving with an acceleration