Gr XIIndian Language School2018-19

Worksheet-1Properties of Bulk Matter- Elasticity

  1. A steel wire of length 4 m and diameter 5 mm is stretched by 5 Kg.wt. Find the increase in its length if young’s modulus of steel wire is 2.4 x 1012 dyne/cm2 0.0041 cm
  2. A steel wire of diameter 2 mm can withstand a maximum strain of 10-3. Find the maximum load it can hold. Y steel = 2 x 10 11 N/m2 628 N
  3. A steel rod has radius of 10 mm and a length of 1 m. A 100 KN Force stretches it along its length. Find (i) stress (ii) elongation (iii) strain on the rod Y steel = 2 x 10 11 N/m2

3.18 x 108 N/m2. 1.59 mm, 1.59 mm

  1. The cross sectional area of steel wire is 1 cm2. What is the force required to double the length of the wire. Y steel = 2 x 10 11 N/m2 2 x 107 N
  2. The ratio of radii of 2 wires of same material is 2:1. If these wires are stretched by equal force, find the ratio of stress produced in them. 1:4
  3. Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown. The unloaded length of steel wire is 1.5 m and that of brass wire is 1 m. compute the elongation of steel and brass wire. 0.15 mm, 0.13 mm
  1. A 5 cm cube has its upper surface displaced by 0.2 cm by a tangential force of 8 N. Calculate the shearing strain, shearing stress and modulus of rigidity of the material of the cube. 4,3200 N/m2, 8x 104 N/m2
  2. When the pressure on the sphere is increased by 80 atm then its volume decreases by 0.01 %. Find the bulk modulus of elasticity of the material of the sphere. 8.1 x 1010 N/m2
  3. Find the change in volume which 1 m3 of water undergo, taken from the surface to the bottom of the sea 1 Km deep. Given the elasticity of water is 20.000 atm. 4.8x 10-3 m3
  4. A solid ball 3 cm in diameter is submerged in a lake to a depth, where the pressure is 103Kgfm-3. Find the change in volume of the ball, if the bulk modulus of the material of the ball is 107 dyne/cm3. 0.138 cm3
  5. A rubber cube of side 7cm has one side fixed, while a tangential force of 200Kgf is applied to the opposite face. Find the shearing strain produced and the distance through which the strained side moves.(modulus of rigidity of rubber =2X106Nm-2) 0.2 rad, 1.42 cm
  6. A brass wire 2.5 mm long with area of cross section 1x 10-3 cm2is stretched 1 mm by a load of 0.40 Kg. Calculate the young’s modulus of brass. What percentage of strain does the wire suffer? Use the value of Y to calculate the force required to produce 4 % of strain in the same wire.9.8x1010Nm-2, 0.040 %, 15.68 x 10-2 N
  7. A steel has a square cross section 10 mm X 10 mm and a length of 2 m. Calculate the strain energy when a stress of 400 M Pa is produced by stretching it. Y= 2 x 109 N/m2 80 J
  8. A structural member is subjected to a stress of 8x 1012 N/m2 and a 4% strain. What is the strain energy developed in it? Assume the member to be solid, uniform cylinder of length 8 m and radius 0.35 cm.
  9. The breaking stress of aluminium is 7.5 x 107 N/m2 Find the greatest length of aluminium wire that can hang vertically without breaking. Density of Al is 2.7 x 103 Kg/ m3 2.8 x 103 m
  10. Calculate the strain if the elastic material is stretched to five times its original length.4

Gr XIIndian Language School2017-18

Worksheet-2Properties of Bulk Matter- Elasticity

1)For a material of Young’s modulus 1.25X1014 units, calculate the stress required to produce a 4% strain.

2)A wire suspended vertically from one of its ends is stretched by attaching a weight of 200N to its lower end. The weight stretches the wire by 1mm. find the strain energy stored in the wire.

3)Prove that the potential energy of a stretched spring is proportional to the square of the extension.

4)Show that the strain energy per unit volume is half the product of stress and strain.

5)Discuss fully the stress –strain curve of an elastic material.

6)What is the basic equation employed in echo location?

7)Name two instruments used in measuring mass and the kind of mass they measure.

8)Describe the triangulation method of locating inaccessible objects.

1)What is the common assumption on which error analysis is based?

2)Give that A = P3 express the percentage error in A in terms of the percentage error in P.

3)Define the term young’s modulus and give its units.

4)What is meant by bulk modulus of rigidity?

5)Define elastic fatigue.

6)Show that the strain energy in a stretched spring is proportional to the square of its extension.

7)The Young’s modulus of a material is 7.5X1012units. what is the stress required to cause a 2 percent strain?

8)A student measures the following dimensions of a cylinder:

a)Height : 6cm ±0.8%

b)Radius : 0.35cm ±1%

Calculate the absolute and percentage error in the surface area of the cylinder.

9)A cube of aluminium of each side 4cm is subjected to a tangential force. The top face of the cube is sheared through 0.012cm with respect to the bottom face. Calculate (i) shearing strain, (ii) shearing force. Given ɳ = 2.25X1010Nm-2 for aluminium.

10)Prove that :

Strain energy per unit volume = X(stress)X(strain)