Physics · Textbook solutions

Mechanical Properties of Solids

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 53 questions

6. Mechanical Properties of Solids — worked examples

5 q

Solved Examples

Worked · 5
  1. Solved Ex.6.1
    A brass wire of length 4.5 m with crosssectional area of 3×10−53 \times 10^{-5} m2^{2} and a copper wire of length 5.0 m with cross sectional area 4×10−54 \times 10^{-5} m2^{2} are stretched by the same load. The same elongation is produced in both the wires. Find the ratio of Young's modulus of brass and copper.
  2. Solved Ex.6.2
    A wire of length 20 m and area of cross section 1.25×10−41.25 \times 10^{-4} m2^{2} is subjected to a load of 2.5 kg. (1 kgwt = 9.8 N). The elongation produced in wire is 1×10−41 \times 10^{-4} m. Calculate Young's modulus of the material.
  3. Solved Ex.6.3
    A metal cube of side 1 m is subjected to a force. The force acts normally on the whole surface of cube and its volume changes by 1.5×10−51.5 \times 10^{-5} m3^{3}. The bulk modulus of metal is 6.6×10106.6 \times 10^{10} N/m2^{2}. Calculate the change in pressure.
  4. Solved Ex.6.4
    Calculate the modulus of rigidity of a metal, if a metal cube of side 40 cm is subjected to a shearing force of 2000 N. The upper surface is displaced through 0.5 cm with respect to the bottom. Calculate the modulus of rigidity of the metal.
  5. Solved Ex.6.5
    The coefficient of static friction between a block of mass 0.25 kg and a horizontal surface is 0.4. Find the horizontal force applied to it.

Exercises

48 q

Choose the correct answer

Practice · 5
  1. 1. Choose the correct answer:
    Ex Q.1 (i)
    Change in dimensions is known as…..
    1. A.
      deformation
    2. B.
      formation
    3. C.
      contraction
    4. D.
      strain.
  2. Ex Q.1 (ii)
    The point on stress-strain curve at which strain begins to increase even without increase in stress is called….
    1. A.
      elastic point
    2. B.
      yield point
    3. C.
      breaking point
    4. D.
      neck point
  3. Ex Q.1 (iii)
    Strain energy of a stretched wire is 18×10−318 \times 10^{-3} J and strain energy per unit volume of the same wire and same cross section is 6×10−36 \times 10^{-3} J/m3^{3}. Its volume will be....
    1. A.
      3cm3^{3}
    2. B.
      3 m3^{3}
    3. C.
      6 m3^{3}
    4. D.
      6 cm3^{3}
  4. Ex Q.1 (iv)
    ----- is the property of a material which enables it to resist plastic deformation.
    1. A.
      elasticity
    2. B.
      plasticity
    3. C.
      hardness
    4. D.
      ductility
  5. Ex Q.1 (v)
    The ability of a material to resist fracturing when a force is applied to it, is called……
    1. A.
      toughness
    2. B.
      hardness
    3. C.
      elasticity
    4. D.
      plasticity.

Answer in one sentence

Practice · 15
  1. 2. Answer in one sentence:
    Ex Q.2 (i)
    Define elasticity.
  2. Ex Q.2 (ii)
    What do you mean by deformation?
  3. Ex Q.2 (iii)
    State the SI unit and dimensions of stress.
  4. Ex Q.2 (iv)
    Define strain.
  5. Ex Q.2 (v)
    What is Young's modulus of a rigid body?
  6. Ex Q.2 (vi)
    Why bridges are unsafe after a very long use?
  7. Ex Q.2 (vii)
    How should be a force applied on a body to produce shearing stress?
  8. Ex Q.2 (viii)
    State the conditions under which Hooke's law holds good.
  9. Ex Q.2 (ix)
    Define Poisson's ratio.
  10. Ex Q.2 (x)
    What is an elastomer?
  11. Ex Q.2 (xi)
    What do you mean by elastic hysteresis?
  12. Ex Q.2 (xii)
    State the names of the hardest material and the softest material.
  13. Ex Q.2 (xiii)
    Define friction.
  14. Ex Q.2 (xiv)
    Why force of static friction is known as 'self-adjusting force'?
  15. Ex Q.2 (xv)
    Name two factors on which the co-efficient of friction depends.

Answer in short

Practice · 9
  1. 3. Answer in short:
    Ex Q.3 (i)
    Distinguish between elasticity and plasticity.
  2. Ex Q.3 (ii)
    State any four methods to reduce friction.
  3. Ex Q.3 (iii)
    What is rolling friction? How does it arise?
  4. Ex Q.3 (iv)
    Explain how lubricants help in reducing friction?
  5. Ex Q.3 (v)
    State the laws of static friction.
  6. Ex Q.3 (vi)
    State the laws of kinetic friction.
  7. Ex Q.3 (vii)
    State advantages of friction.
  8. Ex Q.3 (viii)
    State disadvantages of friction.
  9. Ex Q.3 (ix)
    What do you mean by a brittle substance? Give any two examples.

Long answer type questions

Practice · 6
  1. 4. Long answer type questions:
    Ex Q.4 (i)
    Distinguish between Young's modulus, bulk modulus and modulus of rigidity.
  2. Ex Q.4 (ii)
    Define stress and strain. What are their different types?
  3. Ex Q.4 (iii)
    What is Young's modulus? Describe an experiment to find out Young's modulus of material in the form of a long straight wire.
  4. Ex Q.4 (iv)
    Derive an expression for strain energy per unit volume of the material of a wire.
  5. Ex Q.4 (v)
    What is friction? Define coefficient of static friction and coefficient of kinetic friction. Give the necessary formula for each.
  6. Ex Q.4 (vi)
    State Hooke's law. Draw a labeled graph of tensile stress against tensile strain for a metal wire up to the breaking point. In this graph show the region in which Hooke's law is obeyed.

Answer the following

Practice · 13
  1. 5. Answer the following Where a value is not stated in the question, take g=9.8g = 9.8 m/s2^{2} — the value this chapter itself uses in Example 6.5. (The book's Exercises print no constants preamble; it is supplied here so that each question can be attempted on its own.)
    Ex Q.5 (i)
    Calculate the coefficient of static friction for an object of mass 50 kg placed on horizontal table pulled by attaching a spring balance. The force is increased gradually it is observed that the object just moves when spring balance shows 50N.
  2. Ex Q.5 (ii)
    A block of mass 37 kg rests on a rough horizontal plane having coefficient of static friction 0.3. Find out the least force required to just move the block horizontally.
  3. Ex Q.5 (iii)
    A body of mass 37 kg rests on a rough horizontal surface. The minimum horizontal force required to just start the motion is 68.5 N. In order to keep the body moving with constant velocity, a force of 43 N is needed. What is the value of a) coefficient of static friction? and b) coefficient of kinetic friction?
  4. Ex Q.5 (iv)
    A wire gets stretched by 4mm due to a certain load. If the same load is applied to a wire of same material with half the length and double the diameter of the first wire. What will be the change in its length?
  5. Ex Q.5 (v)
    Calculate the work done in stretching a steel wire of length 2m and cross sectional area 0.0225mm2^{2} when a load of 100 N is slowly applied to its free end. [Young's modulus of steel =2×1011= 2 \times 10^{11} N/m2^{2}]
  6. Ex Q.5 (vi)
    A solid metal sphere of volume 0.31m3^{3} is dropped in an ocean where water pressure is 2×1072 \times 10^{7} N/m2^{2}. Calculate change in volume of the sphere if bulk modulus of the metal is 6.1×10106.1 \times 10^{10} N/m2^{2}
  7. Ex Q.5 (vii)
    A wire of mild steel has initial length 1.5 m and diameter 0.60 mm is extended by 6.3 mm when a certain force is applied to it. If Young's modulus of mild steel is 2.1×10112.1 \times 10^{11} N/m2^{2}, calculate the force applied.
  8. Ex Q.5 (viii)
    A composite wire is prepared by joining a tungsten wire and steel wire end to end. Both the wires are of the same length and the same area of cross section. If this composite wire is suspended to a rigid support and a force is applied to its free end, it gets extended by 3.25mm. Calculate the increase in length of tungsten wire and steel wire separately. [Given: Ysteel=2×1011Y_{steel} = 2 \times 10^{11} N/m2^{2}, YTungsten=3.40×108Y_{Tungsten} = 3.40 \times 10^{8} N/m2^{2}]
  9. Ex Q.5 (ix)
    A steel wire having cross sectional area 1.2 mm2^{2} is stretched by a force of 120 N. If a lateral strain of 1.455 mm is produced in the wire, calculate the Poisson's ratio. [Given: Ysteel=2×1011Y_{steel} = 2 \times 10^{11} N/m2^{2}]
  10. Ex Q.5 (x)
    A telephone wire 125m long and 1mm in radius is stretched to a length 125.25m when a force of 800N is applied. What is the value of Young's modulus for material of wire?
  11. Ex Q.5 (xi)
    A rubber band originally 30cm long is stretched to a length of 32cm by certain load. What is the strain produced?
  12. Ex Q.5 (xii)
    What is the stress in a wire which is 50m long and 0.01cm2^{2} in cross section, if the wire bears a load of 100kg?
  13. Ex Q.5 (xiii)
    What is the strain in a cable of original length 50m whose length increases by 2.5cm when a load is lifted?