1. A sphere shell of non-conducting material with inner radius a and outer radius b has charge uniformly distributed with a density 1.0x 106 C/m³ (Fig. 1) Plot E-field from r=0cm to 30cm. a=10cm, b=20cm. + + + b + + + ++ ++ Fig. 1
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- Q2)A filament 0.5m long and having a cross-sectional area of 1mm2 was stretched to breaking. If the breaking stress for the filament was found to be 109 Pa, calculate the mass which was hung on the filament to break it. Assuming the filament stretched linearly up to breaking, calculate the amount by which the filament stretched. (Young’s modulus for the material = 6 x 1010 Pa) If the assumption in (b) was justified, what might the material have been? State in one word.184 What is the strain energy of the massless stepped bar as shown in the figure below? [Take E= 200 GPa] (a) 0.38 N-m (c) 0.50 N-m 30 mm 10 mm 100 mm 20 mm 120 mm • ** ** 80 mm 10 kN (b) 0.42 N-m (d) 0.56 N-mJB TIDE blocks The bar shown in the following figure has a diameter of 40 mm and is subjected to a force P = 1500 N and a force F= 500 N. It is made from a material which has a yield strength of 60 MPa, Determine the factor of safety at points A and B using the Von-Mises Theory. 100 mm 50 mm F 2 of 6
- 2.41 The device shown consists of a disk that is rotated by a shaft. The disk is positioned very close to a solid boundary. Be- tween the disk and the boundary is viscous oil. a. If the disk is rotated at a rate of 1 rad/s, what will be the ra- tio of the shear stress in the oil at r = 2 cm to the shear stress at r = 3 cm? b. If the rate of rotation is 2 rad/s, what is the speed of the oil in contact with the disk atr = 3 cm? c. Ifthe oil viscosity is 0.01 N s/m² and the spacing y is 2 mm, what is the shear stress for the conditions noted in part (b)? 2 Pipe Oil film Cylinder PROBLEM 2.40175 mm A 50 mm C -225 mm -300 mm Bar ACB shown in the Figure is subjected to a uniform temperature increase of 35°C. Knowing that the diameters of AC is 50 mm and CD is 75 mm, the modulus of elasticity E is 6.0 GPa, and the thermal expansion coefficient is 100x10^(-6) ?1/°C. What is the displacement of point Ca material has a grain diameter of 0.0005 cm. What height of capillary rise will you expect? The following data applies: The surface tension of water: 73 g/s2 Wetting angle: 0 degrees.
- 2 A rigid bar is supported by two copper ro ds and the gap (A) between the aluminu m rod and the bar is 1.50 mm. If the temp erature for all materials is increased by 4 0 degrees Celsius, what is the thermal str ess of the aluminum rod? Disregard the weight of the rigid bar. For each copper bar, A = 500 mm^2, E = 120 GPa, and a = 1 6.8 μm/(m. C). For the aluminum bar, A = 400 mm^2, E = 70 GPa, and a = 23. 1 μm/(m. C).(5 Copper Aluminum Copper 750 mmA cube 2.28 feet on an edge has its lower half of s.g. = 1.6 and upper half of s.g. = 0.7. It rests in a two layer fluid, with lower s.g. = 1.4 and upper s.g. = 0.8. Determine the height in feet of the top of the cube above the interface.Q.1/Say whether the following statements are true (T) or false (F). Select 10 only: - 1. Ice has crystallographic structure. 2. The term "mafic rocks" means presence of heavy minerals. 3. Contour lines are always parallel. 4. Piezoelectricity results from pressure action. 5. Orthorhombic system contains three unequal and perpendicular axes. 6. The color of mineral Hematite is same as its streak. 7. Equivalents means rocks have same mineral composition but are differing in origin. 8. Cleavage is present in some minerals. 9. The Earth diameter is always constant. 10. Kant theory depend on condensation concept. 11. Presence of coal, lignite or peat reflects open marine environment.
- The steel plate shown below is put in into a rigid chamber, such that spacings of size s 0.00188 m. To fit the plate, it is heated. It can be assumed that the plate can move frictionless along its edges. If x - 4 m and y = 2 m, E = 200 GPa V - 0.28 a = 11.7 x 10 rc When the upper surface of the plate is just about to close with the chamber due temperature increase along y-axis, how much is the stress on its side? Select the correct response:Figure Q4 shows a piece of triangular thin plate ABC with thickness 5 mm. A linear pressure as shown in the figure is being applied to edge AB with maximum intensity of 100 kN/m² at the middle of edge AB. The plate is made from stainless steel, with a Young's modulus of 200 GPa and Poisson's ratio of 0.3. The deformations in the plate are to be obtained. For such purposes, the finite element method is being employed. (a) (b) (c) (d) (e) State the type of problem involved in this case (to determine the stiffness matrix to be used). Model this problem optimally using the least number of orthogonal triangular elements only. Label the nodes and elements and indicate clearly the status of all the relevant degrees-of- freedom in this model. Set up the appropriate system of simultaneous equations and solve for the unknown displacements. Displacements at point T. Without any calculation, explain on the value of strain at points S and T.Find the value of strain energy of metallic bar with cross sectional area of 2 cm² and gauge length of 10 cm if it stretches 0.002 cm under the load of 10 kN? 1. 14 N-cm 2. 12 N-cm 3. 16 N-cm 4. 10 N-cm