MCQOPTIONS
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MCQOPTIONS
This section includes 35 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mechanics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Polar radius of gyration for a circular lamina of diameter d is equal to |
| A. | \(\frac{d}{{2\sqrt 2 }}\) |
| B. | \(\frac{d}{{3\pi }}\) |
| C. | \(\frac{{4d}}{\pi }\) |
| D. | \(\frac{d}{8}\) |
| Answer» B. \(\frac{d}{{3\pi }}\) | |
| 2. |
A rectangular section has 200 mm depth and 300 mm in width. Determine Moment of Inertia about the centroidal axis parallel to the width. |
| A. | 450 × 106 mm4 |
| B. | 200 × 106 mm4 |
| C. | 300 × 106 mm4 |
| D. | 600 × 106 mm4 |
| Answer» C. 300 × 106 mm4 | |
| 3. |
Moment of inertia of a circular area, whose diameter is d, about an axis perpendicular to the area, passing through its centre is given by: |
| A. | \(\frac{\pi d^4}{64}\) |
| B. | \(\frac{\pi d^4}{32}\) |
| C. | \(\frac{\pi d^4}{14}\) |
| D. | \(\frac{\pi d^4}{24}\) |
| Answer» C. \(\frac{\pi d^4}{14}\) | |
| 4. |
Moment of inertia of a triangle of base width ‘b’ and height ‘h’ with respect to the centroidal axis parallel to its base is equal to: |
| A. | \(\frac {bh^3}{12}\) |
| B. | \(\frac {bh^3}{18}\) |
| C. | \(\frac {bh^3}{24}\) |
| D. | \(\frac {bh^3}{36}\) |
| Answer» E. | |
| 5. |
Moment of inertia of a rectangular section having width (b) and depth (d) about an axis passing through its centre of gravity and parallel to the depth, is- |
| A. | bd3/36 |
| B. | db3/36 |
| C. | bd3/12 |
| D. | db3/12 |
| Answer» E. | |
| 6. |
Moment of inertia of a rectangular plate of width b and height h about the centroidal axis is |
| A. | \(\frac{{b{h^2}}}{3}\) |
| B. | \(\frac{{{b^3}h}}{6}\) |
| C. | \(\frac{{b{h^3}}}{{12}}\) |
| D. | \(\frac{{{b^3}h}}{{12}}\) |
| Answer» D. \(\frac{{{b^3}h}}{{12}}\) | |
| 7. |
A circular disc rolls down without slipping on an inclined plane. The ratio of its rotational kinetic energy to the total kinetic energy is |
| A. | 1/4 |
| B. | 1/2 |
| C. | 1/3 |
| D. | 2/3 |
| Answer» D. 2/3 | |
| 8. |
According to theorem of perpendicular axes, Ixx and Iyy be the M.I. of a lamina about xx and yy axis, then M.I. of the lamina about axis zz, which is perpendicular to xx and yy, equal to |
| A. | Ixx × Iyy |
| B. | Ixx + Iyy |
| C. | \(\frac{{{{\text{I}}_{{\text{xx}}}}}}{{{{\text{I}}_{{\text{yy}}}}}}\) |
| D. | \(\frac{{{{\text{I}}_{{\text{yy}}}}}}{{{{\text{I}}_{{\text{xx}}}}}}\) |
| Answer» C. \(\frac{{{{\text{I}}_{{\text{xx}}}}}}{{{{\text{I}}_{{\text{yy}}}}}}\) | |
| 9. |
Moment of inertia of hollow rectangular section having outer depth 'D' and breadth 'B' and dimensions of inner rectangle are depth ‘d’ and width 'b' about horizontal axis passing through centroid is: |
| A. | \(\frac{BD^3}{12}\) |
| B. | \(\frac{bd^3}{12}\) |
| C. | \(\frac{{B{D^3}\;-\;b{d^3}}}{{12}}\) |
| D. | \(\frac{{B{D^2}\;-\;b{d^2}}}{{12}}\) |
| Answer» D. \(\frac{{B{D^2}\;-\;b{d^2}}}{{12}}\) | |
| 10. |
A spherical shape has a diameter 'D', its moment of inertia (MI) will be - |
| A. | πD4 / 64 |
| B. | πD3 / 64 |
| C. | πD2 / 64 |
| D. | πD4 / 32 |
| Answer» B. πD3 / 64 | |
| 11. |
Moment of inertia (about its neutral axis) of hollow rectangular section with overall width and depth as B and D and hollow rectangular hole as b and d is |
| A. | \(\frac{(BD^3\;-\;bd^3)}{16}\) |
| B. | \(\frac{(BD^3\;-\;bd^3)}{32}\) |
| C. | (BD3 – bd3) |
| D. | \(\frac{(BD^3\;-\;bd^3)}{12}\) |
| Answer» E. | |
| 12. |
Moment of Inertia of a triangular section, about an axis passing through its centre of gravity and parallel to the base, is ____. |
| A. | bh3/12 |
| B. | bh3/36 |
| C. | bh3/32 |
| D. | None of these |
| Answer» C. bh3/32 | |
| 13. |
Moment of inertia of quarter circle of radius 'r' about 'x' axis passing through centroid is : |
| A. | IX = 0.055r4 |
| B. | IX = 0.11r4 |
| C. | IX = 0.4r4 |
| D. | None of these |
| Answer» B. IX = 0.11r4 | |
| 14. |
Area moment of inertia of a circular section of diameter D is? |
| A. | \(\frac{{{\rm{\pi }}{{\rm{D}}^3}}}{{32}}\) |
| B. | \(\frac{{{\rm{\pi }}{{\rm{D}}^4}}}{{32}}\) |
| C. | \(\frac{{{\rm{\pi }}{{\rm{D}}^3}}}{{64}}\) |
| D. | \(\frac{{{\rm{\pi }}{{\rm{D}}^4}}}{{64}}\) |
| Answer» E. | |
| 15. |
According to perpendicular axis theorem, |
| A. | Izz = Ixx + Iyy |
| B. | Izz = Ixx + ah2 |
| C. | Izz = Ixx × Iyy |
| D. | Izz = (Ixx)2 + (Iyy)2 |
| Answer» B. Izz = Ixx + ah2 | |
| 16. |
A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre O as shown in figure. The moment of inertia of the loop about the axis XX’ is |
| A. | \(\frac{{\rho {L^3}}}{{16{\pi ^2}}}\) |
| B. | \(\frac{{\rho {L^3}}}{{8{\pi ^2}}}\) |
| C. | \(\frac{{5\rho {L^3}}}{{16{\pi ^2}}}\) |
| D. | \(\frac{{3\rho {L^3}}}{{8{\pi ^2}}}\) |
| Answer» E. | |
| 17. |
M.I. of a triangular section of base a and height h about an axis passing through its c.g. and parallel to base is |
| A. | \(\frac{{{\rm{a}}{{\rm{h}}^3}}}{8}\) |
| B. | \(\frac{{{\rm{a}}{{\rm{h}}^3}}}{12}\) |
| C. | \(\frac{{{\rm{a}}{{\rm{h}}^3}}}{24 }\) |
| D. | \(\frac{{{\rm{a}}{{\rm{h}}^3}}}{36}\) |
| Answer» E. | |
| 18. |
Moment of inertia of a circular section of radius ‘R’ about its diametrical axis is: |
| A. | \(\dfrac{\pi R^4}{64}\) |
| B. | \(\dfrac{\pi R^4}{32}\) |
| C. | \(\dfrac{\pi R^4}{4}\) |
| D. | \(\dfrac{\pi R^4}{8}\) |
| Answer» D. \(\dfrac{\pi R^4}{8}\) | |
| 19. |
Determine the centroid (xc, yc) of the shaded area as shown in figure with respect to given coordinate axes |
| A. | \(\left( {b,\;\frac{{28 + 3\pi }}{{3\left( {8 + \pi } \right)}}} \right)\) |
| B. | \(\left(b,\frac{(20\;+\;3\pi)b}{3(8\;+\;\pi)}\right)\) |
| C. | \(\left( {b,\;\frac{{5 }}{{\left( {8 + \pi } \right)}}}b \right)\) |
| D. | \(\left( {b,\;\frac{{1 + 2\pi }}{{2\left( {8 + \pi } \right)}}}b \right)\) |
| Answer» C. \(\left( {b,\;\frac{{5 }}{{\left( {8 + \pi } \right)}}}b \right)\) | |
| 20. |
An Aluminium object is made of a solid cone of height ‘h’ and base diameter D attached to a solid cylinder of diameter D and height ‘h/2’ as shown in figure. It is kept inclined touching to a vertical wall at point ‘A’ and hinged at point B on the floor. The object stays in this inclined position without going to vertical position (axis perpendicular to the floor), only if θ is less than |
| A. | tan-1(10 D/9h) |
| B. | π/2 – sin-1 (10 D/h) |
| C. | π/2 – sin-1 (10 D/9h) |
| D. | tan-1 (20 D/9h) |
| Answer» D. tan-1 (20 D/9h) | |
| 21. |
Centroid of a semi-circle with diameter ‘d’ will be at a distance of _____ from the base diameter. |
| A. | \(2d\over4π\) |
| B. | \(4π\over 3d\) |
| C. | \(2d\over 3π\) |
| D. | \(3d\over 2π \) |
| Answer» D. \(3d\over 2π \) | |
| 22. |
Centre of gravity of a thin hollow cone lines on the axis of symmetry at a height of _____. |
| A. | one-half of the total height above base |
| B. | one-third of the total height above base |
| C. | one-fourth of the total height above base |
| D. | None of these |
| Answer» C. one-fourth of the total height above base | |
| 23. |
A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their centre of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true? |
| A. | The ring has higher kinetic energy |
| B. | The disc has higher kinetic energy |
| C. | The ring and the disc have the same kinetic energy |
| D. | Kinetic energies of both the bodies are zero since they are not in linear motion |
| Answer» B. The disc has higher kinetic energy | |
| 24. |
Moment of inertia of a thin spherical shell of mass M and radius R, about its diameter is |
| A. | \(MR^2\) |
| B. | \(\frac{1}{2}MR^2\) |
| C. | \(\frac{2}{5}M{R^2}\) |
| D. | \(\frac{2}{3}M{R^2}\) |
| Answer» E. | |
| 25. |
Area moment of inertia for the quadrant shown below is : |
| A. | \(\frac{{\pi {r^4}}}{2}\) |
| B. | \(\frac{{\pi {r^4}}}{4}\) |
| C. | \(\frac{{\pi {r^4}}}{8}\) |
| D. | \(\frac{{\pi {r^4}}}{{16}}\) |
| Answer» E. | |
| 26. |
Moment of inertia of a uniform circular disc of mass M and radius R about an axis passing through its Centre of gravity is |
| A. | MR2 |
| B. | 0.5 MR2 |
| C. | 2 MR2 |
| D. | 2.5 MR2 |
| Answer» C. 2 MR2 | |
| 27. |
Moment of inertia of a rod having mass M and length L about an axis XX is |
| A. | \(\frac{{M{l^2}}}{9}\) |
| B. | \(\frac{{M{l^2}}}{12}\) |
| C. | \(\frac{{4M{l^2}}}{9}\) |
| D. | Ml2 |
| Answer» B. \(\frac{{M{l^2}}}{12}\) | |
| 28. |
Moment of inertia of a square of side d about the diagonal is |
| A. | \(\frac {a^4}{18}\) |
| B. | \(\frac {a^4}{24}\) |
| C. | \(\frac {a^4}{12}\) |
| D. | \(\frac {a^4}{8}\) |
| Answer» D. \(\frac {a^4}{8}\) | |
| 29. |
An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the centre of mass is v, the kinetic energy of the disc is |
| A. | \(\frac{9}{{16}}m{v^2}\) |
| B. | \(\frac{{11}}{{16}}m{v^2}\) |
| C. | \(\frac{{13}}{{16}}m{v^2}\) |
| D. | \(\frac{{15}}{{16}}m{v^2}\) |
| Answer» D. \(\frac{{15}}{{16}}m{v^2}\) | |
| 30. |
Moment of inertia of an area always least with respect to |
| A. | Bottom-most axis |
| B. | Radius of gyration |
| C. | Vertical axis |
| D. | Centroidal axis |
| Answer» E. | |
| 31. |
A rigid body shown in the first figure has a mass of 10 kg. It rotates with a uniform angular velocity ‘ω’. A balancing mass of 20 kg is attached as shown in second figure. The percentage increase in mass moment of inertia as a result of this addition is |
| A. | 25% |
| B. | 50% |
| C. | 100% |
| D. | 200% |
| Answer» C. 100% | |
| 32. |
Moment of inertia of triangular section having base 80 mm and height 60 mm about axis passing through CG and parallel to base is |
| A. | 15 × 106 mm4 |
| B. | 20 × 106 mm4 |
| C. | 480 × 103 mm4 |
| D. | 1440 × 103 mm4 |
| Answer» D. 1440 × 103 mm4 | |
| 33. |
Moment of inertia (second moment of area) of triangular lamina about base and centroidal axis (parallel to base), respectively will be ______ and _______ [ b = length of base of triangular section, h = Height of triangular section] |
| A. | \(\frac{{b{h^3}}}{3},\frac{{b{h^3}}}{{36}}\) |
| B. | \(\frac{{b{h^3}}}{{36}},\frac{{b{h^3}}}{{12}}\) |
| C. | \(\frac{{b{h^3}}}{{12}},\frac{{b{h^3}}}{{36}}\) |
| D. | \(\frac{{b{h^3}}}{3},\frac{{b{h^3}}}{{12}}\) |
| Answer» D. \(\frac{{b{h^3}}}{3},\frac{{b{h^3}}}{{12}}\) | |
| 34. |
If the two axes about which the product of inertia is found, are such that the product of inertia becomes zero, the two axes are called as |
| A. | centroidal axes |
| B. | principal axes |
| C. | major and minor axes |
| D. | none of the above |
| Answer» C. major and minor axes | |
| 35. |
Consider a trapezoidal lamina ABCD, with AB parallel to DC, 6 cm apart; AB is 8 cm; CD is 12 cm; CD extends outwards by 1 cm from the foot of the perpendicular from B on DC. The centre of gravity of the lamina will be |
| A. | Along AC at a height of 3 cm form DC |
| B. | Along BD at a height of 3 cm from DC |
| C. | Along the line joining the mid-point of AB to the mid-point of DC, at a height of 2.8 cm from DC |
| D. | At the inersection point of AC and DB |
| Answer» D. At the inersection point of AC and DB | |