TRB BT Assistant - Friction, Equilibrium and Centre of Gravity Question Bank with Options

1. A particle is in equilibrium if the resultant of all forces acting on it is:

A) Equal to its weight

B) Equal to its mass

C) Zero

D) Infinite

2. If the coefficient of static friction is 0.6, what is the angle of repose?

A) Approximately 30.96 degrees

B) Approximately 31.00 degrees

C) Approximately 59.04 degrees

D) Approximately 60.00 degrees

3. What is the angle of repose?

A) The maximum angle of inclination at which a body remains at rest.

B) The minimum angle of inclination at which a body starts to slide.

C) The angle between the applied force and the normal.

D) The angle between the friction force and the resultant force.

4. The center of gravity of a non-uniform rod is:

A) Always at its geometrical center

B) Closer to the heavier end

C) Closer to the lighter end

D) At one of its ends

5. A uniform plank is supported at its ends. If a person walks along the plank, the condition for equilibrium requires that the total downward force must be balanced by the total upward force, and the net torque about any point must be:

A) Maximum

B) Minimum

C) Zero

D) Constant

6. Lami's Theorem applies to a system of ______ coplanar forces in equilibrium.

A) Two

B) Three

C) Four

D) Any number of

7. Which factor does NOT affect the force of friction between two dry surfaces?

A) The nature of the surfaces

B) The normal force pressing the surfaces together

C) The relative velocity between the surfaces

D) The coefficient of friction

8. If a block is pulled with a force F on a rough surface, and the block remains at rest, the friction is:

A) Equal to F

B) Equal to limiting friction

C) Less than F

D) Zero

9. The condition for a body resting on a rough inclined plane to remain in equilibrium is that the angle of inclination (α) must be less than or equal to the:

A) Angle of repose

B) Angle of friction

C) Both angle of repose and angle of friction

D) Critical angle

10. When a body is pushed over a rough horizontal surface, the work done by friction is:

A) Positive

B) Negative

C) Zero

D) Infinite

11. Which type of equilibrium is achieved when a ball is placed at the bottom of a hemispherical bowl?

A) Stable

B) Unstable

C) Neutral

D) Incomplete

12. The center of gravity of a body is the point where the resultant force of ______ acts.

A) Applied forces

B) Frictional forces

C) Gravitational forces

D) Normal forces

13. If a body is in equilibrium, its:

A) Linear momentum is changing

B) Angular momentum is changing

C) Linear momentum is constant

D) Angular momentum is zero

14. For a system to be in equilibrium, the net external force must be zero. This is a condition for:

A) Rotational equilibrium

B) Translational equilibrium

C) Both translational and rotational equilibrium

D) Mechanical equilibrium

15. A body is in equilibrium under the action of three coplanar forces. If these forces are represented by the sides of a triangle taken in order, this is known as:

A) Newton's first law

B) Lami's theorem

C) The triangle law of forces

D) The parallelogram law of forces

16. Which of the following statements about friction is incorrect?

A) Friction opposes relative motion or tendency of motion.

B) Friction depends on the nature of the surfaces in contact.

C) Friction is independent of the area of contact.

D) Friction is directly proportional to the applied force.

17. The friction between the surfaces of a tyre and the road is an example of:

A) Sliding friction

B) Static friction

C) Rolling friction

D) Fluid friction

18. Consider a block on a horizontal surface. If the applied horizontal force is increased gradually, the friction force:

A) Remains constant

B) Increases up to the limiting value, then decreases

C) Decreases gradually

D) Becomes zero immediately

19. The center of gravity of a cone is located at a height of ______ from its base.

A) h/4

B) h/3

C) h/2

D) 2h/3

20. Which of the following conditions must be satisfied for a rigid body to be in equilibrium?

A) Sum of forces = 0

B) Sum of torques = 0

C) Sum of forces = 0 AND Sum of torques = 0

D) Sum of forces = 0 OR Sum of torques = 0

21. If a body is subjected to multiple forces and is in equilibrium, then the algebraic sum of the components of these forces along any direction is:

A) Maximum

B) Minimum

C) Zero

D) Equal to the net force

22. The relationship between the angle of friction (θ) and the coefficient of static friction (μ_s) is:

A) μ_s = tan(θ)

B) μ_s = sin(θ)

C) μ_s = cos(θ)

D) μ_s = cot(θ)

23. The angle of friction (θ) is defined as the angle between the resultant force and the:

A) Normal reaction

B) Frictional force

C) Applied force

D) Surface

24. A car is parked on a slope. The force preventing it from sliding down is:

A) Kinetic friction

B) Static friction

C) Rolling friction

D) Air resistance

25. What happens to the center of gravity of a person standing on one leg compared to standing on two legs?

A) It is lower

B) It is higher

C) It remains the same

D) It becomes undefined

26. To keep a body in stable equilibrium, its center of gravity should be:

A) As high as possible

B) As low as possible

C) At the same level as the base

D) Above the point of support

27. The center of gravity of a hollow sphere is at its:

A) Inner surface

B) Outer surface

C) Center

D) Base

28. A ladder leaning against a wall is in equilibrium if:

A) Only vertical forces are balanced

B) Only horizontal forces are balanced

C) Both vertical and horizontal forces are balanced, and net torque is zero

D) It is perfectly vertical

29. What condition must be met for rotational equilibrium?

A) Net force is zero

B) Net torque is zero

C) Net momentum is zero

D) Net energy is zero

30. If a body is in equilibrium, what is the net acceleration of the body?

A) Zero

B) Constant and non-zero

C) Variable

D) Depends on the mass

31. The coefficient of static friction (μ_s) is generally ______ the coefficient of kinetic friction (μ_k).

A) Equal to

B) Less than

C) Greater than

D) Independent of

32. Friction is generally considered a ______ force.

A) Conservative

B) Non-conservative

C) Potential

D) Electromagnetic

33. If the applied force is less than the limiting friction, the object will:

A) Start moving

B) Remain at rest

C) Slide backwards

D) Accelerate indefinitely

34. Which of the following is an example of static friction?

A) A car skidding on ice

B) A book resting on a table

C) A block sliding down an inclined plane

D) A ball rolling on the ground

35. A body is in neutral equilibrium if, when slightly displaced, its center of gravity:

A) Rises

B) Falls

C) Remains at the same height

D) Becomes negative

36. In unstable equilibrium, if the body is slightly displaced, its center of gravity:

A) Rises

B) Falls

C) Remains at the same level

D) Becomes infinite

37. For a stable equilibrium, if the body is slightly displaced, its center of gravity:

A) Rises

B) Falls

C) Remains at the same level

D) Becomes zero

38. Where is the center of gravity of a uniform rod located?

A) At one end

B) At the center

C) One-third from an end

D) Two-thirds from an end

39. For a uniform gravitational field, the center of gravity coincides with the:

A) Center of buoyancy

B) Center of mass

C) Centroid

D) Moment of inertia

40. The point where the entire weight of a body can be considered to act is called its:

A) Center of mass

B) Center of gravity

C) Fulcrum

D) Pivot point

41. A body is in equilibrium if it is either at rest or moving with:

A) Uniform acceleration

B) Variable acceleration

C) Constant velocity

D) Zero velocity

42. Rotational equilibrium occurs when the net torque acting on an object is:

A) Zero

B) Maximum

C) Equal to the angular acceleration

D) Constant and non-zero

43. For an object to be in translational equilibrium, the vector sum of all forces acting on it must be:

A) Equal to its mass

B) Equal to its acceleration

C) Zero

D) Constant and non-zero

44. When is an object considered to be in equilibrium?

A) When it is at rest

B) When it is moving with constant velocity

C) When the net force acting on it is zero

D) When it is accelerating

45. What is the formula for the force of kinetic friction (f_k)?

A) f_k = μ_s N

B) f_k = μ_k N

C) f_k = N / μ_k

D) f_k = μ_k / N

46. The force of friction acts in a direction ______ to the applied force.

A) Parallel

B) Perpendicular

C) Opposite

D) At an angle of 45 degrees

47. The maximum value of static friction is called:

A) Limiting friction

B) Kinetic friction

C) Rolling friction

D) Fluid friction

48. Which type of friction opposes motion when two surfaces are in relative motion?

A) Static friction

B) Sliding friction

C) Rolling friction

D) Air friction

49. What is the unit of coefficient of friction?

A) Newton

B) Pascal

C) Dimensionless

D) Meter per second squared

Friction, Equilibrium and Centre of Gravity - Question Bank