MECHANICS

__Short questions__

1) Obtain the dimension of specific heat capacity, latent heat, Universal gas constant, coefficient of viscosity, modulus of elasticity and gravitational constant.

2) The density of the gold is 19.3 gm/cc. Express its value in S.I unit.

3) Taking force, length and time to be fundamental quantities find the dimensional formula for mass, momentum, Universal Gravitational constant and density.

4) Check the correctness of the formula v^{2} =u^{2} +2as using dimensional analysis.

5) Convert 10 ergs in joule.

6) Name any three physical quantities which have same dimensions.

7) Can a quantity have unit but no dimension? Explain.

8) Is dimensionally correct equation necessarily be a correct physical relation? Justify your relation.

9) T force F is given in terms of time‘t’ and displacement ‘x’ by the equation F = Asin*Bx* + Csin*Dt*. What is the dimension of *D/B*?

10) What are the limitations of dimension analysis?

11) Convert 1N into dyne by using dimensional analysis.

12) Can you tell the unit of a physical quantity from its dimensions.

13) Can the sum of the two equal vectors be equal to either of the vectors? Explain.

14) What should be the angle between the two vectors of some magnitude, so that their resultant is equal to either of them?

15) Can the resultant of three vectors be zero?

16) Is pressure a vector? Why?

17) Should a quantity having magnitude and direction be necessarily a vector? Give example.

18) Why are rubbers used as vibration absorbers?

19) Differentiate between elasticity and plasticity.

20) Two wires A and B have equal lengths and are made of same material. If the diameter of wire A is twice that of wire B, which wire has the greater extension for a given load?

21) Why are rubbers used as vibration absorbers?

22) Differentiate between elasticity and plasticity.

23) Two wires A and B have equal lengths and are made up of same material. If the diameter of wire A is twice that of wire B, which wire has the greater extension for a given load?

24) Explain why soldiers are ordered to break steps while crossing a bridge.

25) Compare the mechanical properties of a steel cable, made by twisting many thin wires together, with those of solid steel rod of the same diameter.

26) Explain in terms of breaking stress why elephant has thicker legs as compared to human beings?

27) How will you justify that stone is more rigid than iron?

28) Explain which one is more elastic-rubber or steel.

29) Why bridges are declared unsafeafter a long use?

30) At what distance from the mean position is the K.E equal to P.E in S.H.M

31) A pendulum clock is taken to moon. Will it gain or lose time?

32) How does the frequency vary with amplitude?

33) If a pendulum clock is taken to a mountain top, does it gain or lose time?

34) A pendulum clock is taken to the moon. Will it gain or lose time?

35) If the length of simple pendulum increased by 4 times its original length, will its time period change? If yes, by how much?

36) A pendulum clock is taken to moon. Will it gain or lose time?

37) A pendulum clock is in an elevator that descends at constant velocity. Does it keep correct time? If the same clock is in an elevator in free fall, does it keep correct time?

38) A body is moving in a circular path with constant speed. Is this motion a simple harmonic?

39) Why does the mercury inside the capillary tube made of glass depress when dipped in a reservoir of mercury?

40) Why small drops of mercury are spherical and bigger drops oval in shape?

41) Hairs of a brush spread out when it is dipped in the water and cling together as soon as it is taken out from the water. Explain.

42) We use towels to dry our body after taking a shower, why?

43) Small particles of camphor dance on the surface of water. Why?

44) Hot soup is tastier than the cold one. Why?

45) Why is a soap solution a better cleansing agent than the ordinary water?

46) The tip of the nib of the pen is spilt. Why?

47) What will be the effect on value of acceleration due to gravity, if the earth stops to rotate?

__Long Questions__

1) Explain S.H.M. Obtain an expression for energy of particle executing simple harmoni__c__

2) What is simple pendulum? Show that the motion of simple pendulum is simple harmonic. Also deduce its time period.

3) Show that the motion of loaded vertical spring is simple harmonic. Also find its time period.

4) Explain characteristics of SHM.

5) State and explain triangle law of vector addition.

6) State and explain parallelogram law of vector addition.

7) what is hooks law? Prove it experimentally.

8) Define young’s modulus. Also derive and expression for energy stored in a wire and hence find its energy density.

__Numerical__

1) Calculate the period of oscillation of a simple pendulum of length 1.8 m with a bob of mass 2.2 kg. If the bob of the pendulum is pulled aside a horizontal distance of 20m and released. What will be the value of i) the K.E and ii) the velocity of the bob at the lowest point of the swing.

2) The displacement y of a mass vibrating with a simple harmonic motion is given by y=20sin10πt. Where y is in millimeter and t is in second. What is: (i) amplitude (ii) the period (iii) the velocity at t=0. (0.002m, 0.2s, 0.628m/s)

3) A simple pendulum 4m long swings with an amplitude of 0.2m.Compute the velocity of the pendulum at its lowest point and Compute its acceleration at the end of its path.(0.316m/sec, 0.499m/s^{2})

4) A simple pendulum 5m long swings with an amplitude 25cm. Find the velocity of the pendulum at its lowest point and the acceleration at the end of its path. (0.35m/sec, 0.62m/s^{2})

5) Calculate the period of the oscillation of a simple pendulum of length 1.8m with a bob of mass 2.2kg. If the bob of this pendulum is pulled aside a horizontal distance of 20cm and released. What will be the values of (I) the K.E. and (ii) the velocity of the bob at the lowest point of the swing? (0.243J, 0.47m/s)

6) A simple pendulum 4m long swings with amplitude of 0.2m. Compute the velocity of pendulum at its lowest point at its lowest point and its acceleration at extreme ends. (0.32m/s, 0.5m/s^{2})

7) A particle of mass 0.3kg vibrates with a period of 2 seconds. If its amplitude is 0.5m what is its maximum kinetic energy? (0.37J)

8) A simple pendulum whose length is 1m oscillates 30 times per minute in a certain place. What is the acceleration due to gravity there? (9.87m/s^{2})

9) A pendulum has a period of 4.2 second, when the pendulum is shortened by 1m the period is 3.7 second. From these measurements, calculate the acceleration of free fall and the original length of the pendulum. (10m/s^{2}, 4.5m)

10) A second pendulum is taken to the moon. If the time period on the surface of the moon is 4.9 seconds, what will be the acceleration due to gravity of the moon? Take acceleration due to gravity on the moon to be 1/6^{th} that of the earth. (1.63m/sec^{2})

11) A simple pendulum has a period of 4.2s. When the pendulum is shortened by 1m, the period is 3.7s. From these measurements, calculate the acceleration of free fall g and the original length of the pendulum.

12) If the pendulum is taken from the earth to the moon where the acceleration of free falls is g/6, what relative change, if any occurs in the period T? (2.45:1)

13) A tunnel is dug along the diameter of the earth. If a body is dropped through one end, how much time it would take to reach another end. (42.3min)

14) A small mass rests on a horizontal platform which vibrates in simple harmonic motion with a period of 0.25s. Find the maximum amplitude of the motion which will allow the mass to remain in contact with the platform throughout the motion. (0.0158m)

15) Calculate the work done in stretching a steel wire 100cm in length end of cross sectional area 0/03cm^{2}, when a load is slowly applied without the elastic limit being reached. (Y=3.5x10^{11}N/m^{2}) (8.3x10^{-3}J)

16) Find the work done in stretching a wire of cross sectional area 0.01cm^{2} and 2m long through 0.1mm, if Y for the material of wire is 2x10^{11}N/m^{2}. (5x10^{-4}J)

17) A uniform steel wire of density 7800kg/m^{3} weighs 16 gm and is 250cm. It lengthens by 1.2mm when a load of 80kg is applied. Calculate the value of Young’s modulus for the steel and the energy stored in the wire. (2.0x10^{11}N/m^{2}, 4.8x10^{-2}J)

18) A steel wire of density 8000kg/m^{3} weighs 24gm and 250cm long. It lengthens by 1.2mm when stretched by a force of 80N. Calculate the Young’s modulus for the steel and the energy stored in the wire. (1.4x10^{11}N/m^{2}, 4.8x10^{-2}J)

19) How much force is required to punch a hole 1cm in diameter in a steel sheet 5mm thick whose shearing strength is 2.76x10^{8}N/m^{2}. (4.3x10^{4}N)

20) Convert 10J into erg.

21) The time period of simple pendulum depend on mass, length and acceleration due to gravity. Find the relation for time period.

HEAT AND THERMODYNAMICS

__Short questions__

1) How are gas thermometers superior to mercury thermometers?

2) A thermometer is laid out in direct sun light. Does this thermometer measure the temperature of the air or the sun or what?

3) A faulty thermometer has its fixed points marked 5^{0} and 95^{0. }What is the correct temperature in Celsius when this thermometer reads 59^{0}

4) Show that, Celsius and Fahrenheit thermometer show the same reading at –40^{0}C.

5) Why the column of mercury in a thermometer first descends slightly and then rises when placed in a hot substance?

6) Why is mercury mostly used as thermometric substance?

7) At what temperature do Fahrenheit and Kelvin scale give the same readings?

8) Why are glass windows possible to be cracked in very cold regions?

9) Why measuring scale should be made up of insulators or metals whose coefficient of linear expansion is small?

10) What do you mean by coefficient of linear expansivity? Does it depend upon original length?

11) Why is sometimes possible to loosen caps on screw top bottles by dipping the cap briefly in hot water?

12) Two bodies of same material have the same external diameters and appearance but one is solid and the other is hollow. When they are heated up to same temperature. Is the overall expansion the same?

13) Two bodies of same material have the same external diameters and appearance but one is solid and the other is hollow. When they are heated by same amount of heat. Is the overall expansion the same?

14) Why does heat flow from a body at higher temperature to a body at lower temperature?

15) Frozen water pipes often burst; will a mercury thermometer break if the temperature of the thermometer is brought below the freezing point of mercury?

16) Why are the Polar Regions much cooler than the equatorial regions despite the fact that the Polar Regions are periodically tilted towards sun?

17) Why liquid does has apparent expansion?

18) A hole of 1cm in diameter is drilled in a plate of steel at 20^{0}C. What happens to the diameter of the hole as the steel is heated to 100^{0}C?

__Long Questions__

1) Define linear, superficial and cubical expansivity. Establish the relation between them.

2) What is cubical expansivity? How do you determine the cubical expansivity of liquid by Dulong and Petit's method.

3) Define the terms coefficient of real and apparent expansion of liquid and prove that γ_{r} = γ_{g} + γ_{a} where the symbols have their usual meanings.

4) Define linear and cubical expansivities of solids. Derive an expression for the variation in density of solid when its temperature is raised from ϴ_{1}^{o}C to ϴ_{2} ^{o}C.

5) How do you determine the coefficeint of linear expansion of solid by Pullinger's method? Can same method be used to find the coeffeicnt of superficial expansion of same solid?

__Numerical__

1) A rod is measured to be 20.05 cm long using a steel ruler at a room temperature of 20^{o}c both the rod and the ruler are placed in an oven at 270^{ o}c, where the rod now measures 20.11cm using the same ruler. Calculate the coefficient of thermal expansion for the material of which the rod is made. (α for steel = 11×10^{-6}/^{o}c).

2) A steel tire of internal diameter 0.998m at 15^{o}c is to be fitted on a wheel of diameter 1.00 m. To what temperature must the tire be heated before it can be slipped on? Linear expansivity of steel 12×10^{-6 }/^{o}c

3) An aluminium vessel of capacity 300cc is completely filled with glycerin at 25^{0}C. What volume of glycerin will overflow when the system is heated to 115^{0}C? (Volume expansivity of aluminium is 76.5x10^{–6}/^{0}C and that of glycerin is 5.3x10^{–4}/^{0}C)

4) A glass vessel of volume 50 cm³ is filled with mercury and is heated from 20˚C to 60˚C. What volume of mercury will overflow?(α_{g}=1.8x10ˉ⁶/˚C and γ_{Hg}=1.8x10^{-4}/˚C)

5) A silica bulb of negligible expansivity hold 340 gram of mercury at 0^{o}C when fall. Some steel balls are introduced and remaining space is occupied at 0^{o}C by 255 gram of mercury. On heating the bulb and it’s contents to 100^{o}C, 4.8 gram of mercury overflow. Find the linear expansivity of the steel. ( cubical expansivity of mercury = 180 ×10^{-6}/k)

6) Brass rod of length 0.40m and steel rod of length 0.60m, both are initially at 0.^{0}C are heated to 75^{0}C. If the increase in lengths is the same for both the rods, calculate the linear expansivity of brass. The linear expansivity of steel is 12x10^{–60}C^{–1}.

7) A steel cylinder has an aluminium alloy piston and is at a temperature of 20^{0}C when the internal diameter of the cylinder is exactly 10cm. There is an all round clearance of 0.05mm between the piston and cylinder wall. At what temperature will the fit be perfect? (The linear expansivity of steel and aluminium alloy are 1.2x10^{–5}k^{–1} and 1.6x10^{–5}K^{–1}respectively)

8) A clock which has a brass pendulum beats seconds correctly when the temperature of the room is 30^{0}C. How many seconds will it gain or lose per day when the temperature of the room falls to 10^{0}C? (for brass α= 0.000018^{0}C^{–1})

9) A pendulum clock gains 5sec at 15^{0}C and looses 10sec at 30^{0}C. Find the value of coefficient of linear expansion.

10) A metal rod 30cm long expands by 0.075cm when its temperature is raised from 0^{0}C to 100^{0}C. A rod of different metal and of the same length expands by 0.045cm for the same rise in temperature. A third rod, also 30cm long, is made up of pieces each of the above metals placed end to end, and expands 0.065cm between 0^{0}C and 100^{0}C. Find the length of each portion of the composite bar.

11) An aluminum rod when measured with a steel scale, both being at 25^{0}C appears 1m long. If the scale is correct at 0^{0}C, what is the true length of rod 25^{0}C? what will be the length of rod at 0^{0}C) (α_{al}= 26x10^{–6}/^{0}C and γ_{steel}= 36x10^{–6}/^{0}C)

12) Using the following data, determine the temperature at which a wood will just sink in benzene:

Density of benzene at 0^{0} C (ρ_{b}^{0}) = 9.0 x 10^{2}kg m^{–3}

Density of wood at 0^{0} C (ρ_{w}^{0}) = 88 x 102kg m^{–3}

Cubical expansivity of benzene (γ_{b}^{0}) = 1.2 x 10^{3}K^{–1}

Cubical expansivity of wood (γ_{w}) = 1.5 x 10^{–4 }/k

OPTICS

__Short questions__

- Difference between real image and virtual image.
- Difference between regular and irregular reflection.
- Uses of plane mirror, concave mirror and convex mirror.
- Characteristic of image formed by plane mirror.
- Can a plane mirror ever forms real image?
- Difference between virtual image formed by plane mirror, concave mirror and convex mirror.
- Which mirror is used as a shaving mirror why?
- Why are convex mirrors used in cars for rear view?
- A ray of light is normally incident on a plane mirror, what are the values of glancing angle and angle of deviation?
- What type of mirror is used in search light?
- An ant is approaching a concave mirror with a uniform speed up to focus. How would the speed of image of an ant formed by lens change?
- What is the focal length of plane mirror? Does the mirror formula hold good for a plane mirror?
- A spherical mirror is immersed in water; does its focal length change?
- If you are bringing a plane mirror towards your face at the speed of 10 m/s . at what rate the image is approaching?
- When is formation of real image possible in a convex mirror?
- What is focus? What is the difference between focus and principal focus?
- Prove that the minimum size of plane mirror for a person to see his full image is equal to half of his height.
- Trace the path of rays to locate the image when an object is brought from infinity to pole of a concave mirror.
- Two plane mirrors inclined to each other at an angle 70
^{o.}. A ray is incident on one mirror at angle α. The ray reflected from this mirror falls on the second mirror from where it is reflected parallel to the first mirror. Determine the value of α. - Define: a)luminous flux b) luminous intensity c)iluminance d) lumen e)candela f) inverse square law g) lux
- Why does the illuminance of a surface decrease as it moved away from the light source?
- What is the meaning of Luminous intensity?
- Define luminous flux. State its unit of measurement.

24.What are the factors on which the illuminance of a surface depends?

- Define luminous efficiency of a source of light and give its SI unit.
- What is the difference between lumen and lux?
- Define illuminance. Name the factor upon which it depends.
- The sun is less bright in morning and in evening as compared to that at noon although its distance from the observer is almost the same. Why?
- Distinguish between illuminance and luminance.

__Long questions__

1) State and explain the law of reflection of light and rotation of light.

2) Define focal length and radios of curvature of spherical mirror. How are they related to each other?

3) Define center of curvature. Obtain an expression for mirror formula of concave mirror in the case of virtual image.

4) Obtain mirror formula for concave mirror.

5) Define principal focus. Derive the formula 1/u+1/v =1/f for the convex mirror.

__Numerical__

1) An object 10cm high is placed in front of a convex mirror of focal length 20cm and the object is 30cm fro the mirror. Find the height of the image.

2) A 2cm tall object is placed at 25cm from a concave mirror of focal length 20cm. Find the position, size and nature of the

3) An erect image, three times the size of the object is obtained with a concave mirror of radius of curvature 36cm. What is the position of the object?

4) A concave mirror forms a real image four times as tall as the object placed 10cm in front of mirror. Find the position of the image and radius of curvature of the mirror.

5) It is desired to cast the image of lamp magnified 4 times upon a wall to 40 cm distance from the lamp. What type of spherical mirror is used what is its position?

6) A mirror forms an erect image 30 cm from the object and twice its height. Where must be the mirror situated. What is the radius of curvature, assuming the object real determine whether the mirror concave or convex?

7) A convex mirror of radius of curvature 20 cm forms an image which is half the size of object. Locate the position of the object and image..

8) An object is situated 40 cm from the convex mirror. When a plane mirror is inserted between object and convex mirror at distance of 32 cm from the object. The image of two mirror coccids. What is the focal length of convex mirror?

9) A concave mirror forms, on a screen, an image of twice the linear dimensions of the object. Object and screen are then moved until the image is three times the size of object. If the shift of the screen is 20cm, determine the shift of the object and focal length of the mirror?

10) With a convex mirror, when the object is kept at a distance of 30 cm from the mirror, the image is formed at a distance of 10cm from the mirror. What will be the change in the image distance if the object distance is doubled?

11) A meter scale is placed along the axis of a convex mirror of local length 25cm, its nearer end being at a distance of 50cm. calculate the size of the image formed.

12) A pole 4m long is laid along the principle axis of a convex mirror of focal length 1m. The end of the pole nearer the mirror is 2m from it. Find the length of the image of the pole.

13) A small object placed in front of a spherical mirror gives an image that is real and 4 times the size of object. When the object is moved 10cm towards the mirror a virtual image of the same magnification is formed. Find the focal length of the mirror.

14) A convex mirror with a radius of curvature 30cm, forms real image 20cm from its pole. Explain how it is possible and find whether the image is erect or inverted.

ELECTROSTATICS

__Short questions__

1) What do you mean by electric charge? Explain the basic properties of charge.

2) What do you mean electrification? Explain various method of charging body.

3) How many electrons are combined in 1 coulomb of charge?

4) Calculate the charge carried by 20×10^{18} electrons.

5) Charge of 4.8×10^{-15} C is transformed from the plastic ruler to silk. How many electrons are transformed in this process?

6) What is the total charge of 1Kg electron?

7) A metallic chain is dragged on the ground from a vehicle that carries inflammable materials, why?

8) Why does a photograph record dust particles just after it is cleaned?

9) Electric potential of earth is taken to be zero, why?

10) Why is it dangerous to take shelter under a tree during lightning?

11) Can two electric lines of force ever intersect each other? Explain.

12) Can a conductor be given limitless charge?

13) If an isolated metal sphere is given a positive charge, what would happen to its mass?

14) If an isolated metal sphere is given a negative charge, what would happen to its mass?

15) Why do you sometimes experience a slight electric shock when getting out of your car?

16) Electrostatic experiments do not work well in humid days. Explain

__Long Questions__

1) What do you mean by electrostatic induction? How would you charge a body negatively by induction?

2) What do you mean by electrostatic induction? How would you charge a body positively by induction?

3) What are the properties of charge?

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