Phy 1 (8)

7/26/2019 Phy 1 (8)

http://slidepdf.com/reader/full/phy-1-8 1/10

http://www.rpmauryascienceblog.com/

Q.1. Calculate the amount of energy evolved when eight droplets of mercury (surface tension 0.55 N/m)of radius 1 mm each combine into one.

Q.2. Water is flowing steadily through a horizontal pipe of non-uniform cross-section. If the velocity ofwater at a point where cross-section is 0.02m2 is 2m/s, what is the velocity of water at another pointwhere the cross-section is 0.01 m2?

Q.3. Liquid flows through two capillary tubes connected in series. Their length is L and 2L and radius rand 2r respectively. The pressure difference across the first and second tube is in the ratio.

Q.4. Find the viscous force on a steel ball of 2 mm radius (density 8 g/cc) acquires a terminal velocity of4 cm/s in falling freely in the tank of glycerine (density of glycerine 1.3 g/cc)

Q.5. A body of density B is floating inside a tub of mercury of density

m, such that 60% of the volume of the body is inside mercury.

The volume coefficient of thermal expansion of body is B and

that of mercury ism (= 2

B ). The temperature of the system is

now increased by . Find the fraction of the volume of the bodywhich remains immersed within the mercury.

Q.6. A solid cylinder (cross-sectional area A , length and density 0

) floats on the surface of a liquid of density with its axis verticalas shown. If it is slightly displaced downwards, prove that itsmotion is SHM and determine its time period.

0

0

Q.7. A thick spherical shell having density 2 and outer radius R and inner radius r = 1 3R (3) is thrown

downward inside a tank, containing a liquid having density . Find the time rate of change of speed

of the shell when the speed of the shell becomes

2

0 R gv9

. (Where is the coefficient of

viscosity and g is is is acceleration due to gravity.)

Q.8. A block of metal weighing 10 kg is resting on rough surface ( = 0.4). It

is struck by a jet releasing water at a rate of

2 kg/s and at a speed 8 m/s. Find the velocity of block after 1 sec.

(Assume water comes to rest after striking the block.)

10 kg

=0.4



7/26/2019 Phy 1 (8)



Q.9. A cube of specific gravity 0.6 and side L floats in a rectangular tank

containing water with square base of side 3L. Assume the cube remains

vertical.

(a) Find the ratio of area of the vertical face of cube, which is inside

water to that of vertical face of cube, which is outside water.

(b) Now the tank is accelerated horizontally with acceleration of g 2m s .

Find angle made by water surface with horizontal.

L

2L

3L

Q.10. A long wire of negligible thickness and mass per unit length is floating

in a liquid such that the top surface of liquid dips by a distance ‘y’. If the

length of base of vessel is 2a, find surface tension of the liquid. (y < < a)

y

aa

Q.11. A small ball of radius ‘r’ is falling in a viscous liquid under gravity. Find the dependency of rate ofheat produced in terms of radius ‘r’ after the drop attains terminal velocity.

Q.12. A syringe of diameter D = 8 mm and having a nozzle of

diameter d = 2 mm is placed horizontally at a height of 1.25 m

as shown in the figure. An incompressible and non-viscous

liquid is filled in syringe and the piston is moved at speed of

0.25 m/s. Find the range of liquid jet on the ground.

V=0.25 m/s

h=1.25 m

Q.13. The height of a liquid of density ‘’ in a beaker of area of cross-

section ‘A’ is ‘h0’. Now a block of mass m is floating on the

surface of the liquid. Determine the pressure on the bottom of

the beaker. If atmospheric pressure is P0. h0

P0

m

A

Q.14. A liquid of density ‘’ taken in a cylindrical vessel of diameter ‘’

upto a height of /2 is kept on a horizontal surface. Find the

acceleration with which the vessel should be moved in

horizontal direction so that the level of the liquid at wall ‘AB’

raises to ?

B

A

/2

D

C

Q.15. A liquid drop of certain radius is broken in to 1000 droplets such that each of small drop is having a

radius of 0.5 mm. Find the work done in the process? (T = 70 10-3 N/m).



7/26/2019 Phy 1 (8)


http://www.rpmauryascienceblog.com/ Q.16. A bubble having surface tension T and radius R is formed on a ring

of radius b (b << R). Air is blown inside the tube with velocity v asshown. The air molecule collides perpendicularly with the wall ofthe bubble and stops. Calculate the radius at which the bubbleseparates from the ring.

Rb

v

Q.17. Find the work done to break a drop of water of radius 0.5 cm into identical drops of each of radius 1

mm. (Twater = 7 10-2 N/m).

Q.18. Water flows in a horizontal tube as shown in figure. Thepressure of water changes by 600 N/m2 between A andB where the areas of cross-section are 30 cm2 and 15cm2 respectively. Find the rate of flow of water throughthe tube.

A B

Q.19. A light wooden sphere floats in a liquid such that half of the volume of sphere remains inside the

liquid. Find the ratio of density of liquid to that of sphere.

Q.20. Two identical cylindrical vessels with their bases at the same level each contain liquid of density .

The height of the liquid in one vessel is h 1 and that in the other vessel is h2. The area of either base

is A. Find the work done by gravity in equalizing the levels when the two vessels are connected.

Q.21. If n identical water droplets falling under gravity with terminal velocity v collapse to form a singledrop, which has terminal velocity 4v, find n.

Q.22. A vessel contains oil (density = 0.8 gm/cm3) over mercury (density = 13.6 gm/cm3). A homogeneous

sphere floats with half its volume immersed in mercury and the other half in oil. Find the density of

the material of sphere in gm/cm3.

Q.23. An incompressible non-viscous fluid (density ) flows steadily through a cylindrical pipe which hasradius 2R at point A and radius R at point B (at the same height as A) further along the flowdirection. If the velocity and pressure at point A are v and P respectively, find the pressure at B.

Q.24. A tube of inner radius R1 =1cm open at both end is dipped in the water. A

rod of radius R2 = 8 mm is placed co-axially in the tube as shown in thefigure. If the surface tension of water is T and contact angle is 00. Findthe capillary rise inside tube.



7/26/2019 Phy 1 (8)


http://www.rpmauryascienceblog.com/ Q.25. A cylindrical vessel of thickness 2 cm floats in a

liquid as shown in figure. With a depth of 8 cmimmersed. The vessel develops a leak in itsbottom. What should be minimum height of thevessel so that it may not sink?

D

16 cmh

Q.26. A tank containing a liquid of density and is open

at the top having two identical small holes of

cross-sectional area on the opposite sides. Thedifference in height between the two holes is h.Find out the net horizontal force experienced bythe tank as the liquid comes out of the two holesat initial moment.

h

Q.27. There a cylindrical tank of cross sectional area A resting on a horizontal surface. There is a small

orifice of cross sectional area ‘a’ (a << A) at the bottom lateral surface of it. Initially the tank wasfilled with a liquid of density up to a height of H. Find(a) the speed of the liquid flowing out when the height of the liquid in the tank becomes H/2.(b) the horizontal force required to kept it at rest initially.

Q.28. Siphon is in action in the given figure. The liquidflowing through the siphon has a density of 1.5gm/cc. Calculate the pressure difference betweenpoints B and C.

100 cm

30

B

A

C

20 cm

D

Q.29. A cubical block of iron 5 cm on each side having specific gravity 7.2 is floating on mercury ofspecific gravity 13.6 in a vessel (a) what is the height of the block above mercury level (b) water ispoured into the vessel so that it just covers the iron block. What is the height of water column?

Q.30. Calculate the rate of flow of glycerin of density 1.25 103 kg/m3 through the conical section of ahorizontally placed pipe if the radii of the ends are 0.1 m and 0.04 m and the pressure drop acrossits length is 10 N/m2.

Q.31. A solid cylinder of height h and mass m floats in a

liquid of density as shown in the figure. Now the

cylinder is released inside a liquid of density /4,contained in a downward accelerated vessel. Determinethe magnitude of the acceleration (A) of the vessel, forwhich the cylinder sinks with the relative acceleration(A/3) with respect to the vessel. Neglect all dissipativeforces.

Vessel

at rest

m

h/4



7/26/2019 Phy 1 (8)



Q.32. Two cylindrical tanks of cross-sectional area A1 and A2with their bases at the same level each containing a

liquid of density . The height of liquid in the tanks is H1 and H2, respectively. The tanks are joined togetherthrough a pipe of cross-sectional area ‘a’ as shown inthe figure.Find the time taken to equalize the levels in the tanks

a

H1

A2A1

Q.33. A container of a large uniform cross-section area Aresisting on a horizontal surface, holds two immiscible,

liquids of densities and 2 each of height H. A smallhole of area S (S<<A) is punched on the vertical side ofthe container at a height H/2. (i) Determine initial effluxof the liquid at the hole (ii) time taken by the denserliquid to be emptied upto the level of hole.

H

H

H/2

Q.34. Two spherical bubbles of radii 3 cm and 4 cm coalesce to form another spherical bubble. Calculatethe surface tension of the bubble. The radius of the bubble formed = 4.498 cm and the atmosphericpressure = 105 Pa.

Q.35. A cylindrical vessel of area of cross-section A and filled with liquid to a height of h1 has a capillary

tube of length and radius r protruding horizontally at its bottom. If the viscosity of liquid is ,

density and g = 9.8 m/s2, find the time in which the level of water in vessel falls to h2. [ It is giventhat only in tube viscous force will be present, in cylindrical vessel flow is stream line.]

Q.36. A rod of length 6 m has a mass of 12 kg. It ishinged at end A at a distance of 3m below the

water surface.(i) What weight must be attached to the otherend so that 5m of the rod is submerged?(ii) Find the magnitude and direction of theforce exerted by the hinge on the rod. Thespecific gravity of the material of the rod is 0.5.

B

A

3m



7/26/2019 Phy 1 (8)


http://www.rpmauryascienceblog.com/ Q.37. A rod of length 6 m has specific gravity

(=25/36). One end of the rod is tied to 5m longrope, which in turn is tied to the floor of a pool10 m deep as shown. Find the length of thepart of rod, which is out of water.

10 m5m

Q.38. Water stands at a depth H in a tank whose side-walls are vertical. A hole is made on one of the

walls at a depth h below the water surface. Find at what distance from the foot of the wall does the

emerging stream of water strike the floor and for what value of h this range is maximum?

Q.39. Air is streaming past a horizontal airplane wing such that its speed is 120 m/s at the upper surface

and 90 m/s at the lower surface. If the density of air is 1.3 kg/m2, find the difference in pressure

between the two surfaces of the wing. If the wing is 10m long and has a average width of 2m, thencalculate the gross lift on it.

Q.40. A fixed cylindrical container of cross-section area ‘A’ contains water. A small hole of area ‘a’ (a<<A)is punched on sidewall h height above the bottom at time t = 0. It is found that time taken to reachthe water upto level of hole is T. Find initial height of water level from bottom at time t = 0.

Q.41. Shown in the figure is a container whose top and bottom

diameters are D and d respectively. At the bottom of thecontainer, there is a capillary tube of outer radius b and innerradius a. The volume flow rate in the capillary is Q. If the

capillary is removed the liquid comes out with a velocity of v0.The density of the liquid is given as . Calculate the coefficient

of viscosity .d

D

P

h

Q.42. A block of mass m is kept over a fixed smooth wedge. Block isattached to a sphere of same mass through fixed masslesspulley P1 and P2. Sphere is dipped inside water as shown. Ifspecific gravity of material of sphere is 2, then find theacceleration of the sphere. 30

P1 P2

m

m

Q.43. A non-viscous liquid of constant density 1000kg/m2 flows in astreamline motion along a tube of variable cross section. Thetube is kept inclined in the vertical plane as shown in the figure.The area of cross section of the tube at two points P and Q at

heights of 2 meters and 5 meters are respectively 4 10-3 m2

and 8 10 -3 m2 . The velocity of the liquid at point P is 1 m/s.Find the work done per unit volume by the pressure and thegravity forces as the fluid flows from point P to Q?

Q

P

5m

2m



7/26/2019 Phy 1 (8)


http://www.rpmauryascienceblog.com/ Q.44. Three spherical bubbles each of radius r 1, r 2 and r 3 collapse to form a single spherical bubble of

radius r. Calculate the surface tension of the liquid in terms of r, r 1, r 2 and r 3. Atmospheric pressureis P0. [Assume that temperature remains constant and no leakage of air takes place.]

Q.45. A solid sphere of mass m = 2kg and specific gravity s =0.5 is half stationary relative to a tank filled with water.The tank is accelerating vertically upward withacceleration a = 2m/s-2 (a) Calculate tension in the thread connected betweenthe sphere and bottom of the tank.(b) If the thread snaps, calculate acceleration of spherewith respect to tank.

(Density of water is = 1000 kg m-3)

Q.46. A cylindrical tank having cross-sectional area A = 0.5

m2 is filled with two liquids of density 1 = 900 kgm-3

and 2 = 600 kgm

-3

to a height h = 60 cm each asshown in figure. A small hole having area a = 5 cm2 ismade in right vertical wall at a height y = 20 cm fromthe bottom. Calculate

1

2

B

h

h

A

(i) Velocity of efflux.(ii) Horizontal force F to keep the cylinder in static equilibrium, if it is placed on a smooth horizontalplane and(iii) Minimum and maximum values of F to keep the cylinder in static equilibrium, if coefficient of

friction between the cylinder and the plane is = 0.01. (g = 10 m/s2)

Q.47. A cylindrical tank having cross sectional area A is filled

with two liquids of density 1 and 2 to a height h eachas shown in figure. A small hole having area a is madein right vertical wall at a height y from the bottom.Calculate.

h

h

2

1y

(a) Velocity of efflux(b) Horizontal force F required to keep the cylinder in static equilibrium if it is placed on smoothhorizontal plane.(c) Minimum and maximum values of F to keep the cylinder in static equilibrium if coefficient of

friction between the cylinder and the plane is . (Given that horizontal force F calculated is lessthan the limiting friction).

Q.48. A system of two masses m and 3m

with densities 2 and 3 are

immersed in a liquid of density and also string over a light pulley,which is attached to a point O onthe ceiling. Find the accelerationof the masses.

O

m 3m



7/26/2019 Phy 1 (8)


http://www.rpmauryascienceblog.com/ Q.49. A solid ball of density half that of water falls freely under gravity from a height of 19.6 m and then

enters in water upto what depth will the ball go. How much time will it take to come again to thewater surface. Neglect air resistance and viscosity effects in water,g = 9.8 m/s2.

Q.50. Determine the shape of the jar of the figuregiven below i.e. specify x as function of y sothat water level descends at a constant rateat all times by 4 cm every hour. Given theradius of drain hole is 2mm and can beassumed to be very small compared to x.

drain hole

Q.51. A wide vessel with a small hole at the bottom is filled with water and kerosene. Find the velocity ofthe water flow if thickness of water layer is 30 cm and that of kerosene layer is20 cm. Specific gravity of kerosene = 0.8.

Q.52. To what height should a vessel having square base of dimension L befilled with a homogenous liquid so that the force exerted by the liquid onthe base surface is equal to the force exerted by the liquid on one of theside surface.

L

Q.53. A container of large uniform cross–section area A resting on a horizontalsurface, which contains two immiscible, non–viscous andincompressible liquid of densities d and 2d each of height (H/2) asshown in figure. The lower density liquid is open to the atmospherehaving pressure P0. A tiny hole of cross–sectional areas(s<<A) ispunched on the vertical side of the container at height h(<H/2).Determine (i) the initial speed of efflux of the liquid at the hole (ii) thehorizontal distance x traveled by the liquid initially (iii) the height h M atwhich the hole should be punched so that the liquid traveles themaximum horizontal distance XM initially.

H/2

H/2 h

Q.54. Liquid enters a tube of radius 2 cm with velocity 10 cm/sec.Subsequently it enters another connected tube of radius 1 cm. Twomonometer tubes are attached to these connected tubes of differentcross section (as shown in figure). Find the difference in heights of thelevels of water in monometer tubes.

AB

h



7/26/2019 Phy 1 (8)


http://www.rpmauryascienceblog.com/ Q.55. A metallic plate having shape of square is suspended through

inextensible string from point P. PX is a rigid rod clamped through X onvertically fixed rod as shown in the figure. The plate is completelyimmersed in the water such that level of water is well above the plate.The clamp X is then slowly raised vertically up with a constant velocityalong the fixed rod. Determine the curve between tension T in the stringand the displacement S of clamp X (with proper explanation).

xP

Q.56. A cylindrical vessel of cross sectional area A2 is filled with water up to height H m. There is smallhole at the bottom lateral surface of the cylinder having cross sectional area A1 (A1<<A2). Find thetime in which the water will drain out through hole.

Q.57. A wooden plank of length 1m and uniform cross section is hinged at oneend to the bottom of the tank as shown in figure. The tank is filled with waterup to height of 0.5 m. The specific gravity of the plank is 0.5. Find the angle

that the plank makes with the vertical in the equilibrium position.

B

0.5 m

B

Hing

Q.58. A wooden ball of density D is immersed in water of density d (d>D) to a depth h below the surface

of water and then released. Find

(a) Maximum height attained by ball from its initial position.

(b) Find time taken by ball to reach maximum height.

Neglect the time for which ball was in partial contact with water and air.

Q.59. A uniform solid cylinder of density 0.8 g/cm3 floats in equilibrium in acombination of two non-mixing liquids A and B with its axis vertical.

The densities of the liquids A and B are 0.7 g/cm3 and 1.2 g/cm3,

respectively. The height of liquid A is h A = 1.2 cm. The length of the

part of the cylinder immersed in liquid B is hB = 0.8 cm.

(a) Find the total force exerted by liquid A on the cylinder.

(b) Find h, the length of the part of the cylinder in air.

(c) The cylinder is depressed in such a way that its top surface is just

below the upper surface of liquid A and is then released. Find the

acceleration of the cylinder immediately after it is released.

A

B

air h

h A

hB

Q.60. A long cylindrical vessel of radius 2R contain liquid of viscosity . A

solid cylinder of radius R is submerged in the water it can rotate freely

about its axis. Find the net torque required to rotate cylinder with

angular velocity 0 if velocity gradient is assumed to be constant to be

constant for arrangement shown in figure.

2R

R

0

h2

h1



7/26/2019 Phy 1 (8)


http://www.rpmauryascienceblog.com/ Q.61. A metal sphere of mass m having cavity inside has an instantaneous upward acceleration a when

released from rest fully submerged in a liquid of density d1. Taking the density of the metal as d2,find the volume of the cavity in the sphere.

Q.62. (a) Find the terminal velocity of a rain drop of radius 0.01 mm. The coefficient of viscosity of air is

1.0 10-5 N-s/m2 and its density is 0.1 kg/m3. Density of water = 1000 kg/m3.(b) Two soap bubbles of radii r 1 and r 2 coalesce under isothermal conditions to form a new bubble.If T is the surface tension of the soap solution, then calculate the radius of the new bubble.

Q.63. A long capillary tube of radius b is dipped vertically into water. Thewater rises to certain height in capillary tube. If another longcapillary tube of radius a (a < b) is dipped in water in the capillarytube of radius b symmetrical. Find (i) change in height of water intube of radius b. (ii) Find the height of water in small tube. (Assumecontact angle to be zero).

b

a

Q.64. An open tank containing a non-viscous liquid to a height of 5m is placed over the ground. A heavyspherical ball falls from height 40 m over the ground in the tank. Ignoring air resistance find theheight to which ball will go back. Collision between ball and bottom of tank is perfectly elastic.

Q.65. A cylindrical tank of height 0.4 m is open at the top and has a dimeter 0.16 m. Water is filled in it up

to a height of 0.16 m. Find out the time taken to empty the tank through a hole of radius 5 10-3 m

at the bottom.



Phy 1 (8)

Documents

Transcript of Phy 1 (8)