MCQOPTIONS
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MCQOPTIONS
This section includes 72 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. |
Frictional force is more in |
| A. | dry sliding friction |
| B. | dry rolling friction |
| C. | non-viscous friction |
| D. | viscous friction |
| Answer» B. dry rolling friction | |
| 2. |
A body of mass 10 kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is 0.3. The body slides down the plane and attains a velocity of 20 m/s. The distance travelled (in metre) by the body along the plane is close to |
| A. | 4.8 |
| B. | 98 |
| C. | 41 |
| D. | 9.8 |
| Answer» D. 9.8 | |
| 3. |
If W is weight of a body, α is angle of an inclined plane and ϕ is angle of friction, then the force required to drag the body when it is just impending to move the plane, is_____ |
| A. | W tan(α + ϕ) |
| B. | W cos(α + ϕ) |
| C. | W sin(α + ϕ) |
| D. | W sec(α + ϕ) |
| Answer» B. W cos(α + ϕ) | |
| 4. |
A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the Y-Y axis, stands on a rough level floor as shown in the figure. A force P is applied at mid-height on the wardrobe so as to tip it about point Q without slipping. What are the minimum values of the force (in Newton) and the static coefficient of friction μ between the floor and the wardrobe, respectively? |
| A. | 490.5 and 0.5 |
| B. | 981 and 0.5 |
| C. | 1000.5 and 0.15 |
| D. | 1000.5 and 0.25 |
| Answer» B. 981 and 0.5 | |
| 5. |
Friction between two surfaces in contact depends on |
| A. | Bending moment |
| B. | Area of contact between the surfaces |
| C. | Energy possessed by the surfaces |
| D. | Equal and opposite normal reaction between surfaces |
| Answer» E. | |
| 6. |
A weight of 500 N is held on a smooth plane, inclined at 30° to the horizontal by a force P acting 30° above the plane as shown in the figure below. The reaction of the plane on the weight will be: |
| A. | 500 N |
| B. | 250 N |
| C. | 476 N |
| D. | 288 N |
| Answer» E. | |
| 7. |
A wedge M and a block N are subjected to forces P and Q as shown in the figure. If force P is sufficiently large, then the block N can be raised. The weights of the wedge and the block are negligible compared to the forces P and Q. The coefficient of friction (μ) along the inclined surface between the wedge and the block is 0.2. All other surfaces are frictionless. The wedge angle is 30°. The limiting force P, in terms of Q, required for impending motion of block N to just move it in the upward direction is given as P = αQ. The value of the coefficient 'α' (round off to one decimal place) is |
| A. | 0.6 |
| B. | 2 |
| C. | 0.5 |
| D. | 0.9 |
| Answer» E. | |
| 8. |
If the resultant R, of two forces P and Q acting at an angle θ makes an angle α with P, then |
| A. | \({\tan~\alpha} =\left[ {\frac{{{\rm{P}}\sin {\rm{\theta }}}}{{{\rm{Q}}~ -~ {\rm{P}}\sin {\rm{\theta }}}}} \right]{\rm}\) |
| B. | \({\tan~\alpha} =\left[ {\frac{{{\rm{Q}}\sin {\rm{\theta }}}}{{{\rm{P}} ~+~ {\rm{Q}}\cos {\rm{\theta }}}}} \right]{\rm}\) |
| C. | \({\tan~\alpha} =\left[ {\frac{{{\rm{P}}\sin {\rm{\theta }}}}{{{\rm{P}} ~+~ {\rm{Q}}\sin {\rm{\theta }}}}} \right]{\rm}\) |
| D. | \({\tan~\alpha} =\left[ {\frac{{{\rm{P}}\cos {\rm{\theta }}}}{{{\rm{P}} ~+~ {\rm{Q}}\sin {\rm{\theta }}}}} \right]{\rm}\) |
| Answer» C. \({\tan~\alpha} =\left[ {\frac{{{\rm{P}}\sin {\rm{\theta }}}}{{{\rm{P}} ~+~ {\rm{Q}}\sin {\rm{\theta }}}}} \right]{\rm}\) | |
| 9. |
A bucket of water of 50 kg is lifted vertically upwards with a uniform acceleration of 0.5 m/s2 (g = 10 m/s2). Calculate the tension in the rope. |
| A. | 525 N |
| B. | 475 N |
| C. | 25 N |
| D. | 52.5 N |
| Answer» B. 475 N | |
| 10. |
A block weighing W = 20 kN is resting on an inclined plane which makes an angle of 30° to the horizontal. The component of gravity force parallel to the inclined plane is |
| A. | 5 kN |
| B. | 17.32 kN |
| C. | 10 kN |
| D. | 14.14 kN |
| Answer» D. 14.14 kN | |
| 11. |
A solid block ‘A’ weighing ‘Q’ kg is resting on a flat floor. A smooth cylinder ‘B’ weighing ‘P’ kg. is placed between the solid A and the vertical wall as shown in fig. The friction between the cylinder, wall and the block A is negligible. The co-efficient of friction between the block A and floor is μ. The minimum weight P required to disturb the block A is |
| A. | \(\frac{{Q\left( {1 - \tan \theta } \right)}}{{\mu \tan \theta }}\) |
| B. | \(\frac{{\mu Qtan\theta }}{{\left( {1 - \mu \tan \theta } \right)}}\) |
| C. | μ Q cos θ |
| D. | \(\frac{{\mu Q}}{{\cos \theta }}\) |
| Answer» C. μ Q cos θ | |
| 12. |
A rectangular block is resting inside a circular tunnel as shown. The reaction at the contacts P and Q are directed |
| A. | Along PQ |
| B. | Perpendicular to PQ |
| C. | Through the center of mass of the block |
| D. | Through the center of the circular tunnel |
| Answer» E. | |
| 13. |
"If three forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between the other two."The above theorem is known as: |
| A. | Pythagoras theorem |
| B. | Lami's theorem |
| C. | Kummer's theorem |
| D. | Hamilton's theorem |
| Answer» C. Kummer's theorem | |
| 14. |
In rigid body mechanism, equilibrium should satisfy with respect to |
| A. | Only forces |
| B. | Both forces and moments |
| C. | Energy |
| D. | Geometry |
| Answer» C. Energy | |
| 15. |
If point A is in equilibrium under the action of the applied forces, the values of tension. TAC = ? |
| A. | 520 N |
| B. | 150 N |
| C. | 400 N |
| D. | 450 N |
| Answer» D. 450 N | |
| 16. |
If there is no change in pressure at any point of the system with time, then the system is said to be in: |
| A. | chemical equilibrium |
| B. | thermal equilibrium |
| C. | phase equilibrium |
| D. | mechanical equilibrium |
| Answer» E. | |
| 17. |
If two forces each equal to P in magnitude act at right angles, their effect may be neutralized by a third force acting along their bisector in opposite direction whose magnitude is equal to |
| A. | 2P |
| B. | P/2 |
| C. | √2P |
| D. | P/√2 |
| Answer» D. P/√2 | |
| 18. |
Four forces of magnitudes 20 N, 40 N, 60 N and 80 N are acting respectively along the four sides of a square ABCD as shown in figure. The magnitude of resultant is |
| A. | 40√2 N |
| B. | 50√2 N |
| C. | 45√2 N |
| D. | 60√2 N |
| Answer» B. 50√2 N | |
| 19. |
A block weighting 100 N is resting on a plane inclined with horizontal as shown in Fig. What horizontal force P is necessary to hold the body from sliding down the plane? (Coefficient of friction can be taken as 0.25) |
| A. | 30 N |
| B. | 120 N |
| C. | 60 N |
| D. | 15 N |
| Answer» D. 15 N | |
| 20. |
A wooden block of mass 10 kg is at rest initially as shown in the figure. A linearly time varying force is applied. The static and kinematic coefficients of friction are 0.6 and 0.4, respectively. The velocity of the block at t = 4s in m/s will be (take g = 10 m/s2): |
| A. | 5 |
| B. | 0 |
| C. | 6.4 |
| D. | 7.5 |
| Answer» D. 7.5 | |
| 21. |
In three dimensional analysis, equilibrium of parallel forces along x-axis requires |
| A. | ∑Fx = 0, ∑Fy = 0, ∑Fz = 0 |
| B. | ∑Fx = 0, ∑Mx = 0, ∑My = 0 |
| C. | ∑Fx = 0, ∑My = 0, ∑Mz = 0 |
| D. | ∑Fx = 0, ∑Fy = 0, ∑Mz = 0 |
| Answer» D. ∑Fx = 0, ∑Fy = 0, ∑Mz = 0 | |
| 22. |
Parallel forces have their lines of action: |
| A. | transverse to each other |
| B. | parallel to each other |
| C. | tangential to each other |
| D. | perpendicular to each other |
| Answer» C. tangential to each other | |
| 23. |
A ladder is resting on a smooth ground and leaning against a rough vertical wall. The force of friction will act |
| A. | towards the wall at its upper end |
| B. | away from the wall at its upper end |
| C. | downward at its upper end |
| D. | upward at its upper end |
| Answer» E. | |
| 24. |
A steel ball of mass 2.4 kg is tied to a string and whirled it in a horizontal plane in a circle of diameter 2 m at a constant speed of 20 rpm. The tension in the string is (ignore gravity) |
| A. | 5 N |
| B. | 10.5 N |
| C. | 100 N |
| D. | 50.5 N |
| Answer» C. 100 N | |
| 25. |
An elastic rod, 30 cm long, of negligible weight, hangs downwards from support. In one case load is applied on rod 20 cm below the support and in the other case the same load is applied at bottom of the rod. The reactions at supports will be |
| A. | More in first case |
| B. | Same in both the cases |
| C. | More in second case |
| D. | None of the above |
| Answer» C. More in second case | |
| 26. |
A block of mass M, supporting another block of mass m, is moved horizontally with an increasing acceleration from zero. If μ is the coefficient of static friction between the blocks, the acceleration at which the upper block slips on the lower block is |
| A. | μm/g |
| B. | μg |
| C. | \(\frac{{\mu mM}}{{m\;+\;M}}\) |
| D. | None of the above |
| Answer» C. \(\frac{{\mu mM}}{{m\;+\;M}}\) | |
| 27. |
If three forces, acting at a point, be in equilibrium then each force is proportional to the sine of the angle between the other two. This theorem is called |
| A. | Law of triangle of forces |
| B. | Law of parallelogram of forces |
| C. | Lami's theorem |
| D. | Trigonometrical theorem |
| Answer» D. Trigonometrical theorem | |
| 28. |
A weight of 200 N is to be pulled over a surface with a coefficient of friction 0.2. What is the force needed to start the motion? |
| A. | 1000 N |
| B. | 40 N |
| C. | 200.2 N |
| D. | 199.2 N |
| Answer» C. 200.2 N | |
| 29. |
Condition of static equilibrium of a planar force system is written as |
| A. | ΣF = 0 |
| B. | ΣM = 0 |
| C. | ΣF = 0 and ΣM = 0 |
| D. | None of these |
| Answer» D. None of these | |
| 30. |
Crowning of pulley is done to |
| A. | Increase the tightness of the belt on the pulley |
| B. | Prevent the belt running off the pulley |
| C. | Increase the torque transmitted |
| D. | Improve shape and strength of pulley |
| Answer» C. Increase the torque transmitted | |
| 31. |
A body of weight 50 kN rests in limiting equilibrium on a rough plane, whose slope is 30°. The plane is raised to a slope of 45°. Find the value of the coefficient of friction for equilibrium |
| A. | 0.577 |
| B. | 0.749 |
| C. | 0.623 |
| D. | 0.425 |
| Answer» B. 0.749 | |
| 32. |
Four forces having magnitudes of 200 N, 400 N, 600 N and 800 N respectively acting along four sides (1 m each) of a square ABCD as shown in Figure. Determine the magnitude and direction of the resultant force from A along the line AB. |
| A. | 400√3 N, 3.2 m from A |
| B. | 400√2 N, 2.5 m from A |
| C. | 300√2 N, 2 m from A |
| D. | 300√3 N, 2.5 m from A |
| Answer» C. 300√2 N, 2 m from A | |
| 33. |
An elephant is stopped by a rope wound twice around the rough trunk of a tree. If the elephant exerts a pull of 1000 kgf, the minimum force required to stop the elephant is_____. (Coefficient of friction between the rope and the tree is 0.3) |
| A. | 1000 kgf |
| B. | 300 kgf |
| C. | 700 kgf |
| D. | 23 kgf |
| Answer» E. | |
| 34. |
A 5 m long ladder is resting on a smooth vertical wall with its lower end 3 m from the wall. What should be the coefficient of friction between the ladder and the floor for equilibrium? |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{3}{8}\) |
| C. | \(\frac{1}{3}\) |
| D. | \(\frac{3}{5}\) |
| Answer» C. \(\frac{1}{3}\) | |
| 35. |
A beam is fixed at one end and is vertically supported at the other end. What is the degree of statical indeterminacy? |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 36. |
A truss with two bars PR and QR, making angles α and β, respectively, with the vertical, is shown in the figure below. The connections at P, Q and R are hinged connections. The truss supports a body of weight W (in N) at R as shown. The tension in the bar QR (in N) is |
| A. | \(\dfrac{W \rm sin{\beta}}{\rm cos{\left( \alpha+\beta\right)}}\) |
| B. | \(\dfrac{W \rm cos{\beta}}{\rm sin{\left( \alpha+\beta\right)}}\) |
| C. | \(\dfrac{W \rm cos{\alpha}}{\rm cos{\left( \alpha+\beta\right)}}\) |
| D. | \(\dfrac{W \rm sin{\alpha}}{\rm sin{\left( \alpha+\beta\right)}}\) |
| Answer» E. | |
| 37. |
If two equal forces of magnitude P acts at an angle \(\theta\), their resultant will be |
| A. | \(\frac{P}{2} \cos \theta\) |
| B. | \(2P \cos (\frac{\theta }{2})\) |
| C. | \(2P \sin (\frac{\theta }{2})\) |
| D. | \(\frac{P}{2} \sin \theta\) |
| Answer» C. \(2P \sin (\frac{\theta }{2})\) | |
| 38. |
In free body diagrams, the Principle of transmissibility states that the force acting on the body is a: |
| A. | wedging vector |
| B. | unit vector |
| C. | rolling vector |
| D. | sliding vector |
| Answer» E. | |
| 39. |
Force F in the given figure equals to |
| A. | 1 kN |
| B. | 2 kN |
| C. | 1.73 kN |
| D. | 4 kN |
| Answer» D. 4 kN | |
| 40. |
If three coplanar concurrent forces acting at a point ‘O’ are in equilibrium then ratios of forces \(\frac{T_1}{T_2}\) & \(\frac{T_1}{T_3}\) respectively are, |
| A. | \(\sqrt3\) and \(\sqrt{\frac{3}{2}}\) |
| B. | \(\sqrt {\frac{3}{2}} and \sqrt 3\) |
| C. | 1 and \(\frac{1}{2}\) |
| D. | \(\frac{1}{2}\) and 1 |
| Answer» B. \(\sqrt {\frac{3}{2}} and \sqrt 3\) | |
| 41. |
According to the law of moments, if a number of coplanar forces acting on a particle are in equilibrium, then- |
| A. | The algebraic sum of their moments about any point in their plane is zero |
| B. | Their lines of action are at equal distances |
| C. | The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point |
| D. | Their algebraic sum is zero |
| Answer» D. Their algebraic sum is zero | |
| 42. |
In the figure shown, the minimum ratio of μ1/μ2 so that the masses move together with the application of force F is |
| A. | 5 |
| B. | 2 |
| C. | 4 |
| D. | 3 |
| Answer» E. | |
| 43. |
A body is pulled up on an inclined plane of inclination 20° to the horizontal. The angle of friction between the body and the plane is 17°. The force required to pull the body up the plane is minimum when it is applied: |
| A. | At angle of 20° to the plane |
| B. | At angle of 17° to the plane |
| C. | In the horizontal direction |
| D. | Along the plane |
| Answer» C. In the horizontal direction | |
| 44. |
A 1 m long uniform beam of 2 kg mass is being lifted vertically up by a force F at the 100 cm mark. What is the minimum force required to do so? |
| A. | 1 N |
| B. | 2 N |
| C. | 10 N |
| D. | 20 N |
| Answer» D. 20 N | |
| 45. |
If the sum of all the forces acting on a body is zero, it may be concluded that the body |
| A. | Must be in equilibrium |
| B. | May be in equilibrium |
| C. | May be in equilibrium provided that forces are concurrent |
| D. | May be in equilibrium provided that forces are parallel |
| Answer» D. May be in equilibrium provided that forces are parallel | |
| 46. |
A force f = (10î + 8ĵ - 5k̂) acts a point P(2, 5, 6). What will be the moment of the force about the point Q(3, 1, 4)? |
| A. | – 36î + 15ĵ - 48k̂ |
| B. | 18î + 19ĵ - 37k̂ |
| C. | 32î - 31ĵ - 4k̂ |
| D. | Zero |
| Answer» B. 18î + 19ĵ - 37k̂ | |
| 47. |
A short cylinder of circular cross-section and weight N is resting on a V block of angle 2α as shown in the figure. The reaction at point A is |
| A. | \(\frac{W}{2}\) |
| B. | \(\frac{W}{{2\sin \alpha }}\) |
| C. | \(\frac{W}{{2\cos \alpha }}\) |
| D. | \(\frac{{W\sin \alpha }}{2}\) |
| Answer» C. \(\frac{W}{{2\cos \alpha }}\) | |
| 48. |
Consider a truss PQR loaded at P with a force F as shown in the figure. The tension in the member QR is |
| A. | 0.5 F |
| B. | 0.63 F |
| C. | 0.73 F |
| D. | 0.87 F |
| Answer» C. 0.73 F | |
| 49. |
A 10 kg mass is hung from 2 light, inextensible strings as shown. The tension in the horizontal string is nearly |
| A. | 49 N |
| B. | 57 N |
| C. | 100 N |
| D. | 0 N |
| Answer» C. 100 N | |
| 50. |
A weight of 500 N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respectively: |
| A. | 433 N and 250 N |
| B. | 250 N and 433 N |
| C. | 353.5 N and 250 N |
| D. | 250 N and 353.5 N |
| Answer» B. 250 N and 433 N | |