Properties of matter Questions and Answers

1 Calculate the density specific weight and specific volume of chlorine gas at 25 C and under a pressure of 600 kPa absolute The gas constant R for chlorine is 117 kJ kg K and g 9 81 m s

A steel cable hanging vertically can support a maximum load W If the cable is cut to exactly half of its original length then the maximum load that it can support now is OW W 2 2W More than but less than W

Two opposite forces F 120N and F 80N act on an heavy elastic plank of modulus of elasticity y 2x10 1 N m2 and length L 1m placed over a smooth horizontal surface The cross sectional area of plank is A 0 5m2 If the change in the length of plank is x x 10 m then find x F F 1

A cantilever beam AB of length L and uniform flexural rigidity El has a rigid bracket BC attached to its free end as shown in the figure End C is subjected to a vertically downward force P If deflection at point B is zero then should be 12 213 A 12 D 1

15 A rod of length 1 05m having negligible mass is supported at its ends by two wires of steel wire A and aluminium wire B of equal lengths as shown in figure the cross sectional areas of wires A and B are 1 mm and 2mm respectively The young s modulus of steel wire is 200 x 10 pa and that of aluminium wire is 70 x 10 pa You are supposed to find the point along the rod where the mass m be suspended in order to produce equal stresses and equal strains in both steel and aluminium wires STEEL ROD Ti 1 05 cm Jol 700 a translational b rotational c both d none 2 The ratio of tensions of steel to aluminium wires in the case of equal stresses is ALUMINIUM ROD 1 05 x 1 Which of the following equilibrium helps us in finding the solution to the problem in both cases T

A uniform ring having mass m radius R cross section area of the wire A and young s modulus Y is rotating with an angular speed w is small on a smooth horizontal surface Which of the following options is correct A Tension in the wire is mRo 2 2 B Change in length of the wire is C Change in radius of the ring is mR 2 2A Y 2 2 mR 2 A Y D elastic potential energy stored is 3 1 m w R 4t A Y

A composite rod made of thre and cross section as shown in the fig The thermal conductivities of the materials of the rods are K 2 5K and K respectively The end A and end B are at constant temperatures All heat entering the face A goes out of the end B and there being no loss of heat from the sides of the bar The effective thermal conductivity of the bar is 42 A K 2 1 15K 16 3 5K 16 1 5 C 5K k The figure shows the face and interface temperature of a composite slab containing of four layers of two materials having identical thickness Under steady state condition find the value of temperature 0 20 C 10 C 0 5 C 10 C 2k k 2 6K 13 4 2K 13 2k K k thermal conductivity 2 10 C B

Figure shows a large closed cylindrical tank containing water Initially the air trapped above the water surface has a height ho and pressure 2Po where Po is the atmospheric pressure There is a hole in the wall of the tank at a depth h below the top from which water comes out A long vertical tube is connected as shown Find the distance of water surface in the long tube from the top of the tank when the water stops coming out of the hole 2P Kastnin Sam hohi h

1 4 A steel wire of diameter 2 mm has a breaking strength of 4 x 105 N What is the breaking force of similar steel wire of diameter 1 5 mm 1 2 3 x 105 N 2 2 6 x 105 N 3 3 105 N 4 1 5 105 N

A load of 5 kg hangs from one end of a vertical wire of length 1 m and of radius 1 mm If Young s modulus of the material of the wire is 2 x 1011 N m 2 find the length of the wire when no load is acting on it 10 99 m

ind the minimum diameter of an 1 18 6 m long copper wire that will stretch no more than 9 97 mm when a mass of 371 kg is hung on the lower end Hint The Young s modu f copper is 110 0 GPa

A block of mass M is suspended by a rod of mass M length L area of cross section A and Young s modulus Y Find increment in length of rod 1 2 3 3MgL 2AY MgL 2AY 2MgL AY M Rod M L

A vessel contains 10 kg of ice at 0 C Now steam is passed into the vessel to melt ice Neglecting the thermal capacity of the vessel find the mass of water in the vessel when all ice melts into water 1 12 5 gm 3 112 5 gm 2 100 gm 4 125 gm

16 3 K 4 3K The spring constant of a spring is K When it is divided into n equal parts then what is the spring constant of one part 1 nK 3 nK n 1 2 K n 4 n 1 K n dT The spring

The Young s modulus of brass and steel are 1 x 10 1 N m and 2 x 10 1 N m respectively If wires of both materials having same length are loaded with same weight then they both extend by 4 mm Ratio of the radii of two wires RB Rs is 2 1 1 2 4 1 1 4

6 A uniform rope of length 1 is held motionless on a friction hemisphere of radius r with one end of the rope at the top of hemisphere The hemisphere is made immobile by gluing it on horizontal floor Find where on the rope maximum tensile force developed immediately after the rope is released

A copper wire of diameter 1mm and length 3meters has Young s modulus 12 5 1011 dynes per sq cm If a weight of 10kg is attached to one end what extension is produced If the Poisson s ratio is 0 26 what lateral compression is produced 4

7 Explain origin of friction 8 Derive a relation between Young s modulus coefficient of linear expansion and thermal stres

1 A steel rope of length L area of cross section A Young s modulus Y is hanging from a celling in equilibrium The elastic potential energy per unit volume at a point L 3 from ceiling is Density d A 2 dgL 2 9Y B dgL 2 9Y C 2 dgL 9AY D 2 dgL 7 3Y In the previous probl

ration 5 3 A bar of cross section A is subjected to equal and opposite tensile forces at its ends Consider a plane section of the bar whose normal makes an angle 0 with the axis of the bar F RO F Fig 5 10 a What is the tensile stress on the plane b What is the shearing stress on this plane c For what value of 0 is the tensile stress maximum d For what value of 0 is the shearing stress maximum

Two light wires negligible mass of same dimensions but made of different materials A and B are suspended vertically from one end If the Young s modulus of material A is 25 less than that of material B then the ratio of masses that must be hung from respective wires such that their lower ends are at same level is 8 3 9 1 4 5 3 4

a what is the volume of one molecule of wa ter density 1 g cm b what is the radius of water molecule ass uming it to be spherical c calculated the radius of the oxygen atom assuming that oxygen atom occupies half o f the occupied by the water molecule

liquid of density higher than water is filled in phase of water in a resonance tube to the same level then the frequency of resonance tube will 1 Increase Decrease 3 Remain same 4 Depends on density of liquid

13 The elevator shown in figure 5 E5 is descending with an acceleration of 2 m s The mass of the block A is 0 5 kg What force is exerted by the block A on the block B B 2 m s2 Figure 5 E5

An ideal gas is enclosed in a container of volume V at a pressure P It is being pumped out of the container by using a pump with stroke volume v What is final pressure in container after n stroke of the pump assume temperature remains same 1 P V V V P 3 pVn vn n PV 2 V V 4 P V V V n

If you hang vertically some length of a long uniform inextensible rope the longest hanging length is lo 2 m that does not break due to its own weight Now you cut a length of the rope and place it straight on a horizontal frictionless table with a little length hanging over the edge so that it begins to slide down when released What maximum length can this piece have so that it does not break during sliding

45 B 2 A long elastic cord obeying Hooke s law is stretched considerably due to its own weight In one such case a cord is held from one of its ends and hung vertically and in another case that is shown in the figure the ends are attached to separate nails A and B in the same level so that the cord assume shape of a catenary In which case is the cord stretched longer

Lower end of a capillary tube of radius 10 m is dipped vertically into a liquid Surface tension of liquid is 0 5 N m and specific gravity of liquid is 5 Contact angle between liquid and material of capillary tube is 1200 Choose the correct options use g 10 m s 0 Maximum possible depression of liquid column in the capillary tube is 1 cm Maximum possible depression of mercury column in the capillary tube is 2 cm If the length of the capillary tube dipped inside mercury is half of the maximum possible depression of mercury column in the capillary tube angle made of the mercury surface at the end of the capillary tube with the vertical is cos If the length of the capillary tube dipped inside mercury is one third of the maximum possible depression of mercury column in the capillary tube angle made by the mercury surface at the end of the capillary tube with the vertical is cos

For a certain gas the ratio of specific heats is given to be y 1 5 For this gas 1 C 3 G 3R J 5R 2 Cp 4 C 3R J 5R

A bar of cross section A is subjected to equal and opposite tensile forces F at its ends Consider a through the bar making an angle 0 with a plane at right angles to the bar length a What is the tensile stress at this plane in terms of F A and 0 b What is the shearing stress at this plane in terms of F A and 0 F4 A sie ofte ees F

25 Shown below is a composite rod of metal A and B Their thermal coefficients of linear expansion are a and a2 Their lengths are L and L2 respectively If on heating the length of the entire composite rod does not change then which of the following relations is true A 4 1 2 L L 3 L L 0 B dz 4

Select the correct statement on the basis of the given graph A Young s modulus of A is greater but it is less ductile B Young s modulus of Ais greater and it is more ductile C Young s modulus of A is less and it is less ductile D Young s modulus of A is less but it is more ductile Stress Strain breaking point ion 0 04 mm Breaking

20 A shell is fired vertically upwards with a velocity from a trolley moving horizontally with velocity V A person on the ground observes the motion of the shell as a parabola whose horizontal range is 1 3 2v2V g 2v 2 g 2 4 2v g 2V V 2 g

The volume of an ideal gas at temperature 27 C is changed to 1 th of its initial value adiabatically 4 The new temperature of the gas is y 1 5 1 400 K 2 500 K 3 600 K 4 700 K

10 A uniform slender rod of length L cross sectional area A and Young s modulus Y is acted upon by the forces shown in the figure The elongation of the rod is 3FL A C SAY 3FL BAY B D 2FL 5AY 8FL 3AY 3F L 3 F

12 If Young modulus is three times of modulus of rigidity then Poisson ratio is equal to 4 Can t predict 1 0 2 2 0 3 3 0 4 4 0 5 3 In case of bending of a beam depression depends on Young modulus of elasticity

5 If water be used to construct a barometer what would be the height of water column at standard atmospheric pressure 76 cm of mercury Ja ne

Water flows through the tube shown in figure 13 10 The areas of cross section of the wide and the narrow portions of the tube are 5 cm and 2 cm respectively The rate of flow of water through the tube is 500 cm Find the difference of mercury levels in the U tube

of area 20 cm height 20 cm and volume half a litre va Find the force exerted by the water on the bottom b Considering the equilibrium of the water find the resultant force exerted by the sides of the glass on the water Atmospheric pressure 10 x 10 N m Density of water 1000 kg m and g 10 m s2 Take all num bers to be exact 5 3 2 Ot 20 cm B 20 m Figure 13 E3

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature The length of aluminium rod is acu 1 7 x 10 5 K 1 and Al 2 2 x 10 5 K NEET 2019 1 6 8 cm 3 88 cm 2 113 9 cm 4 68 cm

47 The strain in the upper wire when the whole system moves upwards with an acceleration of 2ms 2 will be Given area of cross section of each string 0 5mm and Y 2x10 NM 2 g 10ms 1 2 104 www T 3Kg T 2Kg 2 4 x 10 4

A wire fixed at the upper end stretches by length by applying a force F The work done i 200 stretching is 1 F 2 3 2F 2 Fl 4 Fl 2

A wire suspended vertically from one of its ends stretched by attaching weight of 200 N to the lower end The weight stretches the wire by 1 mm Then the elastic energy stored in the wire is 2 10 J 4 0 1 J 2003 1 0 2 J 3 20 J

Two blocks of masses m and M are connected by means of a metal wire of cross sectional area A passing over a frictionless fixed pulley as shown in the figure The system is then released If M 2m then the stress produced in the wire is 2mg 3A 1 3 mg A 2 4 4mg 3A 3mg 4A

4 25 An oil drop of 12 excess electrons is held stationary under a constan electric field of 2 55 x 104 NC in Millikan s oil drop experiment The density of the oil is 1 26 g cm Estimate the radius of the drop g 9 81 m s2 e 1 60 x 10 19 C

The breaking stress for a wire of unit cross section is called as 1 Yield point 3 Elastic fatigue 2 Tensile strength 4 Young s modulus

The velocity of water in a river is 18 km h near the surface If the river is 5 m deep find the shearing stress between the horizontal layers of water The co efficient of viscosity of water 10 2 poise a 10 N m 10 N m c 10 N m d 104N m

1 A bead released from one end of a frictionless rigid wire frame fixed in a vertical plane slides periodically on the frame Size of the bead is negligible as compared to the radius of curvature of the turns which is negligible as compared to the length of straight portions of the frame If linear dimensions of the frame are made four times by what factor will frequency of periodic motion of the bead change a 4 c 1 4 b 2 d 1 2

3 Two wires of copper having the length in the ratio 4 1 and their radii ratio as 1 4 are stretched by th same force The ratio of longitudinal strain in the two will be a 1 16 c 1 64 b 16 1 d 64 1

A square frame of ABCD consisting of five steel bars of cross section area 400 mm and joined by pivot is subjected to action of two forces P 40 kN in the direction of the diagonal as shown Find change in angle at A if Young s modulus Y 2 x 105 N mm 1 1 A rad 2000 B 1000 2 1000 C rad D none rad A a 13 40 kN