Work done by constant and variable forces - One Line Questions

1. Work done is a scalar quantity. What is its dimension? — [ML^2T^-2]
2. Which of the following represents the work done by a variable force along a curve in 3D space? — ∫ F ⋅ dr
3. 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: — ∫(x1 to x2) F(x) dx
4. A spring is stretched by 5 cm from its equilibrium position. If the spring constant is 100 N/m, the work done is: — 0.125 J
5. 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? — 50 J
6. If F = (2x + 5) N, the work done in moving a body from x = 0 to x = 1 m is: — 6 J
7. A spring is compressed by 0.1 m. If the spring constant is 200 N/m, what is the work done in compressing it? — 0.5 J
8. 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? — -1/2 kX^2
9. If the velocity of a particle of mass m changes from v1 to v2, the work done by the net force is: — 1/2 m(v2^2 - v1^2)
10. 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: — 7 J
11. A car of mass 1000 kg accelerates from rest to 20 m/s. The work done by the engine is: — 4 x 10^5 J
12. 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): — 200 J
13. Work done by a force F = 3i N on a particle moving along the x-axis from x=1 to x=4 is: — 9 J
14. 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. — 48 J
15. 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? — 10 J
16. For a force F = 5 N and displacement d = 2 m, if the angle between them is 60 degrees, the work done is: — 2.5 J
17. 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? — 50 J
18. What is the work done by gravity when a 5 kg object falls freely from a height of 10 m? — 100 J
19. A force F = (3i + 4j) N acts on a particle and displaces it by d = (2i + 3j) m. Calculate the work done. — 18 J
20. 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? — 18 W
21. If a force F = 4i + 3j N causes a displacement d = 2i + 4j m, the work done is: — 20 J
22. 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: — 27 J
23. Work done by a force is zero when the displacement is perpendicular to the force. Which of the following scenarios exemplifies this? — A porter carrying a load on his head while walking on a horizontal surface.
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? — aL^2 / 2 + bL
25. 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)? — c (1/r2 - 1/r1)
26. Which type of force requires the calculation of work done using integration over a path? — Variable force
27. 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: — Increases
28. 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: — Independent of the path
29. 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: — Force and displacement
30. Which of the following is a conservative force? — Gravitational force
31. The work done by a non-conservative force: — Depends on the path taken.
32. Which of the following is a unit of work, but not a unit of power? — Joule
33. A force F = kx^2 acts on a particle. What is the work done in moving the particle from x = 0 to x = L? — kL^3 / 3
34. The work done in stretching a spring from its equilibrium position by a distance x is given by: — 1/2 kx^2
35. Work done by a force is equal to the change in: — Kinetic energy
36. A body of mass m is moved from rest to a velocity v. The work done by the net force on the body is: — 1/2 mv^2
37. When a block is pulled with a constant force over a rough horizontal surface, the work done by the frictional force is: — Negative
38. 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: — Negative
39. 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: — Zero
40. The work done by the electrostatic force between two charges when they are brought closer is: — Negative
41. What is the work done by a force that does not cause any displacement? — Zero
42. The work done by the gravitational force on a body moving horizontally is: — Zero
43. The work done by the centripetal force in uniform circular motion is: — Zero
44. The work done by the net force on a particle is equal to the change in its: — Kinetic energy
45. If F = 2t^2 i + 3t j, what is the work done by this force from t=0 to t=2s? — This cannot be determined without displacement information.
46. 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? — This cannot be determined without knowing the displacement.
47. What is the SI unit of work done? — Joule
48. When is the work done by a force considered negative? — When the force and displacement are in opposite directions.
49. Which of the following statements is incorrect regarding work done? — Work done is always positive.
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