Work done by constant and variable forces - Question Bank

1. What is the work done by a force that does not cause any displacement?
A) Positive
B) Negative
C) Zero
D) Infinite
2. If F = (2x + 5) N, the work done in moving a body from x = 0 to x = 1 m is:
A) 1 J
B) 3 J
C) 5 J
D) 6 J
3. The work done by the electrostatic force between two charges when they are brought closer is:
A) Positive
B) Negative
C) Zero
D) Depends on distance
4. Which type of force requires the calculation of work done using integration over a path?
A) Constant force
B) Centripetal force
C) Variable force
D) Conservative force
5. If F = 2t^2 i + 3t j, what is the work done by this force from t=0 to t=2s?
A) This cannot be determined without displacement information.
B) 16/3 J
C) 10 J
D) 26/3 J
6. What is the work done by gravity when a 5 kg object falls freely from a height of 10 m?
A) 50 J
B) 100 J
C) -50 J
D) -100 J
7. Work done by a force F = 3i N on a particle moving along the x-axis from x=1 to x=4 is:
A) 3 J
B) 6 J
C) 9 J
D) 12 J
8. A car of mass 1000 kg accelerates from rest to 20 m/s. The work done by the engine is:
A) 2 x 10^5 J
B) 4 x 10^5 J
C) 1 x 10^5 J
D) 4 x 10^6 J
9. If the velocity of a particle of mass m changes from v1 to v2, the work done by the net force is:
A) 1/2 m(v2^2 - v1^2)
B) m(v2 - v1)
C) 1/2 m(v2 - v1)^2
D) m(v2^2 + v1^2)
10. Which of the following is a unit of work, but not a unit of power?
A) Joule
B) Watt
C) Erg
D) Kilowatt-hour
11. For a force F = 5 N and displacement d = 2 m, if the angle between them is 60 degrees, the work done is:
A) 5 J
B) 10 J
C) 2.5 J
D) 7.5 J
12. The work done by the tension in a string when a body tied to it moves in a horizontal circle at a constant speed is:
A) Positive
B) Negative
C) Zero
D) Cannot be determined
13. If a force F = (2x^2 + 1) N acts on a particle, the work done in moving it from x = 0 to x = 3 m is:
A) 9 J
B) 18 J
C) 27 J
D) 30 J
14. A spring is stretched by 5 cm from its equilibrium position. If the spring constant is 100 N/m, the work done is:
A) 0.125 J
B) 0.25 J
C) 0.5 J
D) 1.25 J
15. Which of the following statements is incorrect regarding work done?
A) Work done by a constant force is the dot product of force and displacement.
B) Work done by a variable force is the integral of F ⋅ dr.
C) Work done is always positive.
D) Work done by friction is usually negative.
16. If a force F = 4i + 3j N causes a displacement d = 2i + 4j m, the work done is:
A) 8 J
B) 12 J
C) 20 J
D) 28 J
17. A person lifts a box of mass 10 kg to a height of 2 m. The work done by the person against gravity is approximately (g = 10 m/s^2):
A) 20 J
B) 100 J
C) 200 J
D) 50 J
18. Work done by a force is related to the change in kinetic energy by the work-energy theorem. If the net work done on an object is positive, its kinetic energy:
A) Decreases
B) Increases
C) Remains constant
D) Becomes zero
19. If a force F = 2i + 3j N acts on a particle, and it moves such that its velocity is v = 3i + 2j m/s, what is the instantaneous power delivered by the force?
A) 6 W
B) 12 W
C) 15 W
D) 18 W
20. Work done is a scalar quantity. What is its dimension?
A) [MLT^-1]
B) [ML^2T^-2]
C) [MLT^-2]
D) [ML^2T^-1]
21. A body of mass m is moved from rest to a velocity v. The work done by the net force on the body is:
A) mv
B) 1/2 mv^2
C) mv^2
D) Zero
22. If a force is defined as F(r) = c/r^2 in the radial direction, what is the work done in moving a particle from r1 to r2 (where c is a constant)?
A) c (1/r2 - 1/r1)
B) c (1/r1 - 1/r2)
C) c (r2 - r1)
D) c (r1 - r2)
23. The work done by the net force on a particle is equal to the change in its:
A) Potential energy
B) Kinetic energy
C) Total mechanical energy
D) Linear momentum
24. Consider a force F = (ax + b)i, where a and b are constants. What is the work done in moving a particle from x = 0 to x = L along the x-axis?
A) aL^2 / 2 + bL
B) aL + b
C) aL^2 + bL
D) aL / 2 + b
25. A particle is projected vertically upwards with velocity v. The work done by the gravitational force during its upward journey until it reaches the maximum height is:
A) Positive
B) Negative
C) Zero
D) Depends on the mass
26. Which of the following represents the work done by a variable force along a curve in 3D space?
A) ∫ F ⋅ dr
B) ∫ |F| |dr|
C) ∫ F dr
D) ∫ |F| ⋅ |dr|
27. If a force F acts on an object, and the work done by the force is W, and the displacement is d, then W = Fd cos(θ), where θ is the angle between:
A) Force and acceleration
B) Force and velocity
C) Force and displacement
D) Displacement and acceleration
28. A force F = 5 N is applied to a body at rest. If the body moves a distance of 10 m, what is the work done by the force?
A) 0.5 J
B) 5 J
C) 50 J
D) 10 J
29. Work done by a force is equal to the change in:
A) Momentum
B) Kinetic energy
C) Angular momentum
D) Potential energy
30. If the force acting on a particle is F = -kx, where k is a positive constant, what is the work done by the force when the particle moves from x = 0 to x = X?
A) 1/2 kX^2
B) -1/2 kX^2
C) kX^2
D) -kX^2
31. The work done in stretching a spring from its equilibrium position by a distance x is given by:
A) kx
B) 1/2 kx
C) kx^2
D) 1/2 kx^2
32. A force is represented by the vector F = (2i + j + 3k) N. If a particle moves through a displacement d = (i - j + 2k) m, the work done is:
A) 2 J
B) 1 J
C) 5 J
D) 7 J
33. When a block is pulled with a constant force over a rough horizontal surface, the work done by the frictional force is:
A) Positive
B) Negative
C) Zero
D) Dependent on velocity
34. The work done by a non-conservative force:
A) Is always zero.
B) Is independent of the path.
C) Depends on the path taken.
D) Is always positive.
35. A variable force is given by F = (3x^2 + 2x) N. Calculate the work done by this force when it moves an object from x = 1 m to x = 3 m.
A) 30 J
B) 36 J
C) 42 J
D) 48 J
36. If the force acting on an object is given by F = (2t + 5) N, where t is time in seconds, what is the work done in the first 2 seconds, assuming the object starts from rest?
A) This cannot be determined without knowing the displacement.
B) 14 J
C) 24 J
D) 34 J
37. A force F = kx^2 acts on a particle. What is the work done in moving the particle from x = 0 to x = L?
A) kL^2
B) kL^3 / 3
C) kL^3
D) 3kL^2
38. Work done by a conservative force is independent of the path taken. If a body moves from point A to point B, the work done by a conservative force is:
A) Dependent on the path
B) Independent of the path
C) Always zero
D) Always positive
39. Which of the following is a conservative force?
A) Friction
B) Air resistance
C) Gravitational force
D) Tension in a string
40. The work done by the centripetal force in uniform circular motion is:
A) Positive
B) Negative
C) Zero
D) Variable
41. If a force varies with position as F(x) = 2x + 3, what is the work done in moving an object from x = 0 to x = 2 m?
A) 4 J
B) 6 J
C) 10 J
D) 12 J
42. Work done by a variable force is calculated by integrating the force component along the displacement with respect to displacement. Mathematically, for a force F(x) acting along the x-axis, the work done from x1 to x2 is:
A) ∫(x1 to x2) F(x) dx
B) ∫(x1 to x2) dx / F(x)
C) F(x2) - F(x1)
D) F(x2) * x2 - F(x1) * x1
43. A spring is compressed by 0.1 m. If the spring constant is 200 N/m, what is the work done in compressing it?
A) 1 J
B) 2 J
C) 0.5 J
D) 0.1 J
44. The work done by the gravitational force on a body moving horizontally is:
A) Positive
B) Negative
C) Zero
D) Cannot be determined
45. When is the work done by a force considered negative?
A) When the force and displacement are in the same direction.
B) When the force and displacement are in opposite directions.
C) When the force is perpendicular to the displacement.
D) When there is no displacement.
46. A force F = (3i + 4j) N acts on a particle and displaces it by d = (2i + 3j) m. Calculate the work done.
A) 6 J
B) 12 J
C) 18 J
D) 24 J
47. Work done by a force is zero when the displacement is perpendicular to the force. Which of the following scenarios exemplifies this?
A) A porter carrying a load on his head while walking on a horizontal surface.
B) Pushing a box across a floor.
C) Lifting a weight upwards.
D) Stretching a spring.
48. If a force of 10 N acts on an object and displaces it by 5 m in the direction of the force, what is the work done?
A) 5 J
B) 15 J
C) 50 J
D) 2 J
49. What is the SI unit of work done?
A) Watt
B) Joule
C) Newton
D) Pascal
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