MCQOPTIONS
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MCQOPTIONS
This section includes 70 Mcqs, each offering curated multiple-choice questions to sharpen your Machine Design knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The piston rod of a hydraulic cylinder exerts an operating force of 10kN. The allowable stress in the cylinder is 70N/mm². Calculate the thickness of the cylinder using Clavarinoe’s equation. Diameter of the cylinder is 240mm.μ=0.3 and pressure in cylinder is 15MPa. |
| A. | 35mm |
| B. | 30mm |
| C. | 27mm |
| D. | None of the listed |
| Answer» D. None of the listed | |
| 2. |
The piston rod of a hydraulic cylinder exerts an operating force of 10kN. The allowable stress in the cylinder is 45N/mm². Calculate the thickness of the cylinder using Lame’s equation. Diameter of the cylinder is 40mm and pressure in cylinder is 10MPa. |
| A. | 2.05mm |
| B. | 4.2mm |
| C. | 5.07mm |
| D. | None of the listed |
| Answer» D. None of the listed | |
| 3. |
Lame’s equation is generally used for ductile materials. |
| A. | True |
| B. | False |
| Answer» C. | |
| 4. |
Lame’s equation used to find the thickness of the cylinder is based on maximum strain failure. |
| A. | True |
| B. | False |
| Answer» C. | |
| 5. |
A seamless cylinder of storage capacity of 0.03mᵌis subjected to an internal pressure of 21MPa. The ultimate strength of material of cylinder is 350N/mm².Determine the thickness of the cylinder if it is twice the diameter of the cylinder. |
| A. | 12mm |
| B. | 4mm |
| C. | 8mm |
| D. | 16mm |
| Answer» D. 16mm | |
| 6. |
A seamless cylinder of storage capacity of 0.03mᵌis subjected to an internal pressure of 21MPa. The ultimate strength of material of cylinder is 350N/mm².Determine the length of the cylinder if it is twice the diameter of the cylinder. |
| A. | 540mm |
| B. | 270mm |
| C. | 400mm |
| D. | 350mm |
| Answer» B. 270mm | |
| 7. |
Longitudinal stress in a cylinder is given by [symbols have their usual meanings]. |
| A. | PD/2t |
| B. | 2PD/t |
| C. | PD/4t |
| D. | 4PD/t |
| Answer» D. 4PD/t | |
| 8. |
In an internally pressurized thick cylinder, the hoop stress1. remains constant but the radial stress varies parabolically2. varies parabolically but the radial stress remains constantWhich of the above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» E. | |
| 9. |
A long thin-walled cylindrical shell closed at both ends, is subjected to internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is |
| A. | 0.5 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 10. |
For a thin spherical shell subjected to internal pressure, the ratio of volumetric strain to diametrical strain is _____. |
| A. | 5 : 4 |
| B. | 3 : 2 |
| C. | 2 : 1 |
| D. | 3 : 1 |
| Answer» E. | |
| 11. |
A cylindrical storage tank has an inner diameter of 600 mm and a wall thickness of 18 mm. The transverse and longitudinal strains induced are 255 × 10-6 mm/mm and 60 × 10-6 mm/mm, and if G is 77 GPa, the gauge pressure inside the tank will be |
| A. | 2.4 MPa |
| B. | 2.8 MPa |
| C. | 3.2 MPa |
| D. | 3.6 MPa |
| Answer» E. | |
| 12. |
A spherical shell of 1.2 m internal diameter and 6 mm thickness is filled with water under pressure until volume is increased by 400´103 mm3. If E = 204 GPa, Poisson's ratio v = 0.3, neglecting radial stresses, the hoop stress developed in the shell will be nearly |
| A. | 43 MPa |
| B. | 38 MPa |
| C. | 33 MPa |
| D. | 28 MPa |
| Answer» B. 38 MPa | |
| 13. |
A metal pipe of 1 m diameter contains a fluid having a pressure of 1 N/mm2. If the permissible tensile stress in the metal is 20 N/mm2, then the thickness of the metal required for making the pipe will be: |
| A. | 5 mm |
| B. | 10 mm |
| C. | 15 mm |
| D. | 25 mm |
| Answer» E. | |
| 14. |
Poisson ratio of a thin cylindrical shell is given as \(\frac{1}{m}\), the diameter is ‘d’, length ‘l’, thickness ‘t’ is subjected to an internal pressure ‘p’. Then, the ratio of longitudinal strain to hoop strain is |
| A. | \(\frac{{m - 2}}{{2m + 1}}\) |
| B. | \(\frac{{2m - 1}}{{m - 2}}\) |
| C. | \(\frac{{m - 2}}{{2m - 1}}\) |
| D. | \(\frac{{2m + 1}}{{m - 2}}\) |
| Answer» D. \(\frac{{2m + 1}}{{m - 2}}\) | |
| 15. |
A hub is press fitted on a shaft. An element in the hub is subjected to a radial compressive stress of 50 N/mm2 and hoop stress of 75 N/mm2. If the hub is made of 30C8 steel with yield strength, σy = 350 N/mm2, what is the factor of safety using maximum shear stress theory? |
| A. | 2.8 |
| B. | 3.6 |
| C. | 4.2 |
| D. | 5.6 |
| Answer» B. 3.6 | |
| 16. |
A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is |
| A. | 0.25 |
| B. | 0.5 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 17. |
In thick cylinder, if hoop stress is plotted w.r.t. \(\left( {\frac{1}{{{r^2}}}} \right),\) then the curve will be |
| A. | Parabolic |
| B. | Hyperbolic |
| C. | Linear |
| D. | Elliptical |
| Answer» D. Elliptical | |
| 18. |
In an interference fit between a shaft and a hub, the state of stress or the shaft due to interference fit is |
| A. | Only compressive radial stress |
| B. | a tensile radial stress and a compressive tangential stress |
| C. | a tensile tangential stress and a compressive radial stress |
| D. | a compressive tangential stress and a compressive radial stress |
| Answer» E. | |
| 19. |
A thin spherical shell is subjected to an external pressure po. The volumetric strain of the spherical shell is (where d is the diameter of shell t is the thickness of the shell E is Young’s modulus of elasticity of shell material μ is Poisson’s ratio of shell material). |
| A. | \(\frac{{{p_o}d}}{{4tE}}\left( {5 - 4\mu } \right)\) |
| B. | \(\frac{{3{p_o}d}}{{4tE}}\left( {1 - \mu } \right)\) |
| C. | \(\frac{{3{p_o}d}}{{4tE}}\left( {1 - 2\mu } \right)\) |
| D. | \(\frac{{ - 3{p_o}d}}{{4tE}}\left( {1 - \mu } \right)\) |
| Answer» E. | |
| 20. |
In a thick cylinder, radial stress at inner surface is |
| A. | independent of fluid pressure |
| B. | more than fluid pressure |
| C. | less than fluid pressure |
| D. | equal to fluid pressure |
| Answer» E. | |
| 21. |
A pipe of internal diameter 'd' and thickness of wall 't', carries fluid with intensity of pressure 'p'. Hoop stresses in the wall will be: |
| A. | \(\dfrac{pd}{2}\) |
| B. | \(\dfrac{pd}{4t}\) |
| C. | \(\dfrac{pd}{2t}\) |
| D. | \(\dfrac{pd}{t}\) |
| Answer» D. \(\dfrac{pd}{t}\) | |
| 22. |
A cylinder is considered to be a ‘thin cylinder’, if the thickness to internal diameter of the cylindrical shell is: |
| A. | greater than 1/20 |
| B. | less than 1/10 |
| C. | less than 1/20 |
| D. | greater than 1/10 |
| Answer» D. greater than 1/10 | |
| 23. |
Hoop stress and longitudinal stress in boiler shell under internal pressure are 100 MPa and 50 MPa. Modulus of elasticity and μ are 200 GPa and 0.3 respectively. Hoop strain of boiler is |
| A. | 4.25 × 10-4 |
| B. | 5 × 10-4 |
| C. | 5.8 × 10-4 |
| D. | 7.5 × 10-4 |
| Answer» B. 5 × 10-4 | |
| 24. |
If a thin cylinder is subjected to a fluid pressure of 0.2 N/mm2 whose thickness is 5 mm and diameter is 20 mm. What is the magnitude of Hoop stress generated in it? |
| A. | 0.2 N/mm2 |
| B. | 0.4 N/mm2 |
| C. | 1.4 N/mm2 |
| D. | 0.8 N/mm2 |
| Answer» C. 1.4 N/mm2 | |
| 25. |
A cylindrical pressure vessel has diameter 200 mm and thickness 2 mm. Find the hoop and axial stress (N/mm2) in the cylindrical vessel, when it is subjected to an internal pressure of 5 MPa. |
| A. | 125, 125 |
| B. | 125, 250 |
| C. | 250, 250 |
| D. | 250, 125 |
| Answer» E. | |
| 26. |
A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is |
| A. | 0 |
| B. | 1 |
| C. | 1.08 |
| D. | 2.02 |
| Answer» E. | |
| 27. |
A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average circumferential (hoop) stress in MPa is |
| A. | 100 |
| B. | 250 |
| C. | 500 |
| D. | 1000 |
| Answer» C. 500 | |
| 28. |
A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to withstand a pressure of 25 kg/cm2 should be: |
| A. | 5 cm |
| B. | 10 cm |
| C. | 2.5 cm |
| D. | 1.25 cm |
| Answer» D. 1.25 cm | |
| 29. |
A compressed air spherical tank having an inner diameter of 450 mm and a wall thickness of 7 mm is formed by welding. If the allowable shear stress is 40 MPa, the maximum permissible air pressure in the tank will be nearly |
| A. | 3 MPa |
| B. | 5 MPa |
| C. | 7 MPa |
| D. | 9 MPa |
| Answer» C. 7 MPa | |
| 30. |
A thin-walled cylinder with closed ends for which inner radius is 0.50 meter and outer radius is 0.52 meter, is subjected to internal pressure 2 MPa. The absolute maximum shearing stress on the inner surface of the cylinder shall be |
| A. | 37.5 MPa |
| B. | 75 MPa |
| C. | 26 MPa |
| D. | 24 MPa |
| Answer» D. 24 MPa | |
| 31. |
Design of thin pressure vessel is based on |
| A. | Hoop stress |
| B. | Longitudinal stress |
| C. | Both (1) and (2) |
| D. | None of the above |
| Answer» D. None of the above | |
| 32. |
Oxygen gas at a pressure of 20 MPa is stored in a thin cylinder of thickness 2.5 mm and a mean diameter of 50 mm. The longitudinal stress in the cylinder is |
| A. | 100 MPa |
| B. | 20 MPa |
| C. | 200 MPa |
| D. | 150 MPa |
| Answer» B. 20 MPa | |
| 33. |
A spherical steel pressure vessel 400 mm in diameter with a wall thickness of 20 mm, is coated with a brittle layer that cracks when strain exceeds100 x 10-7. What internal pressure will cause the layer to develop cracks? (E = 200 GPa, µ = 0.3) |
| A. | 0.057 MPa |
| B. | 5.7 MPa |
| C. | 0.57 MPa |
| D. | 57 MPa |
| Answer» D. 57 MPa | |
| 34. |
A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gauge pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is |
| A. | 35 |
| B. | 70 |
| C. | 140 |
| D. | 280 |
| Answer» D. 280 | |
| 35. |
A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.The material of the cylinder has Young’s modulus E. Poisson’s ratio v, and coefficient of thermal expansion α. What is the minimum rise in temperature ΔT of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of p above the atmosphere? |
| A. | \({\rm{\Delta }}T = \frac{{3vpr}}{{2\alpha tE}}\) |
| B. | \({\rm{\Delta }}T = \left( {v - \frac{1}{4}} \right)\frac{{pr}}{{\alpha tE}}\) |
| C. | \({\rm{\Delta }}T = \frac{{vpr}}{{\alpha tE}}\) |
| D. | \({\rm{\Delta }}T = \left( {v + \frac{1}{2}} \right)\frac{{pr}}{{\alpha tE}}\) |
| Answer» D. \({\rm{\Delta }}T = \left( {v + \frac{1}{2}} \right)\frac{{pr}}{{\alpha tE}}\) | |
| 36. |
A thick cylinder of inner dia ‘D’, wall thickness t2 and length ‘L’ is sealed at its both ends with caps. The thickness of the cap is t1. Allowable tensile yield stress = σy and allowable shear stress = τy. A gas is pumped into this cylinder at pressure ‘p’. The cap will yield in shear at circumference of diameter ‘D’ when the gas pressure applied is more than |
| A. | \(\frac{{4{t_1}{\tau _y}}}{D}\) |
| B. | \(\frac{{8{t_1}{\tau _y}}}{D}\) |
| C. | \(\frac{{4{t_2}{\tau _y}}}{D}\) |
| D. | \(\frac{{2{t_1}{\tau _y}}}{D}\) |
| Answer» B. \(\frac{{8{t_1}{\tau _y}}}{D}\) | |
| 37. |
Pressure inside a thin cylindrical vessel of wall thickness ‘t’ and radius ‘r’ is ‘p’. The hoop stress is equal to |
| A. | pr/t |
| B. | (pl/r) |
| C. | πr2p |
| D. | pπr/l |
| Answer» B. (pl/r) | |
| 38. |
Compound tubes are used in internal pressure cases, for following reasons |
| A. | For increasing the thickness |
| B. | For increasing the outer diameter of the tube |
| C. | The strength is more |
| D. | It evens out stresses |
| Answer» E. | |
| 39. |
A water main of 1 m diameter contains water at a pressure head of 100 m. The permissible tensile stress in the material of the water main is 25 MPa. What is the minimum thickness of the water main? (Take g = 10 m/s2) |
| A. | 10 mm |
| B. | 20 mm |
| C. | 50 mm |
| D. | 60 mm |
| Answer» C. 50 mm | |
| 40. |
A thick cylinder, having ro and ri as outer and inner radii, is subjected to an internal pressure P. The maximum tangential stress at the inner surface of the cylinder is |
| A. | \(\frac{P\left( r_{o}^{2}+r_{i}^{2} \right)}{r_{o}^{2}-r_{i}^{2}}\) |
| B. | \(\frac{P\left( r_{o}^{2}-r_{i}^{2} \right)}{r_{o}^{2}-r_{i}^{2}}\) |
| C. | \(\frac{2\text{Pr}_{i}^{2}}{\left( r_{o}^{2}-r_{i}^{2} \right)}\) |
| D. | \(\frac{P\left( r_{o}^{2}-r_{i}^{2} \right)}{r_{i}^{2}}\) |
| Answer» B. \(\frac{P\left( r_{o}^{2}-r_{i}^{2} \right)}{r_{o}^{2}-r_{i}^{2}}\) | |
| 41. |
Hoop stress in a cylindrical pipe of inner diameter 50 mm and wall thickness 2 mm, when subjected to the internal pressure of 1 MPa is |
| A. | 125 MPa |
| B. | 0.01 MPa |
| C. | 12.5 MPa |
| D. | None of the above |
| Answer» D. None of the above | |
| 42. |
A welded steel cylindrical drum made of a 10 mm thick plate has an internal diameter of 1.20 m. Find the change in diameter that would be caused by internal pressure of 1.5 MPa. Assume that Poisson's ratio is 0.30 and E = 200 GPa (longitudinal stress, σy = pD/4t circumferential stress, σx = pD/2t). |
| A. | 4.590 mm |
| B. | 0.459 mm |
| C. | 45.90 mm |
| D. | 0.0459 mm |
| Answer» C. 45.90 mm | |
| 43. |
A hemispherical end of a pressure vessel is fastened to the cylindrical portion of the pressure vessel with help of gaskets, bolts, and lock nuts. The bolts are subjected to. |
| A. | Tensile stress |
| B. | Compression stress |
| C. | Shear stress |
| D. | Bearing stress |
| Answer» B. Compression stress | |
| 44. |
Consider the following statements for a thick-walled cylinder, subjected to an internal pressure:1. Hoop stress is maximum at the inside radius.2. Hoop stress is zero at the outside radius.3. Shear stress is maximum at the inside radius.4. Radial stress is uniform throughout the thickness of the wall.Which of the above statements are correct? |
| A. | 1 and 4 |
| B. | 1 and 3 |
| C. | 2 and 3 |
| D. | 2 and 4 |
| Answer» C. 2 and 3 | |
| 45. |
A steel hub of 100 mm internal diameter and uniform thickness of 10 mm was heated to a temperature of 300°C to shrink fit it on a shaft. On cooling, a crack developed parallel to the direction of the length of the hub. The cause of the failure is attributable to |
| A. | tensile hoop stress |
| B. | tensile radial stress |
| C. | compressive hoop stress |
| D. | compressive radial stress |
| Answer» B. tensile radial stress | |
| 46. |
For a thick-walled shell, the diameter-thickness ratio is |
| A. | less than 20 |
| B. | greater than 20 |
| C. | equal to 20 |
| D. | equal to 10 |
| Answer» B. greater than 20 | |
| 47. |
A thin spherical shell of internal diameter d is subjected to an internal pressure p. if σ is the tensile stress for the shell material, then the thickness of the shell (t) is equal to |
| A. | \(\frac{pd}{2\sigma}\) |
| B. | \(\frac{pd}{4\sigma}\) |
| C. | \(\frac{pd}{\sigma}\) |
| D. | \(\frac{4pd}{\sigma}\) |
| Answer» C. \(\frac{pd}{\sigma}\) | |
| 48. |
In a compound cylinder, hoop stress throughout the metal is- |
| A. | Uniform |
| B. | Variable |
| C. | Zero |
| D. | Maximum |
| Answer» B. Variable | |
| 49. |
A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average hoop stress in MPa is |
| A. | 125 |
| B. | 250 |
| C. | 500 |
| D. | 1000 |
| Answer» C. 500 | |
| 50. |
For thin cylinders |
| A. | Longitudinal stress is double of the circumferential stress |
| B. | Longitudinal stress is half of the circumferential stress |
| C. | Longitudinal stress is equal to the circumferential stress |
| D. | Longitudinal stress is four times of the circumferential stress |
| Answer» C. Longitudinal stress is equal to the circumferential stress | |