Force and Motion—I Problems

This section provides 100 problems to test your understanding of force and motion, including Newton’s laws, the concept of force, applications in linear motion (e.g., blocks, pulleys), and inertial/non-inertial frames. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering dynamics, a core topic for JEE/NEET success.

Numerical Problems

1. A block of mass $4kg$ on a frictionless surface is pushed by a force $F=16N$ horizontally. Calculate the acceleration.

   • (a) $2m/s^2$
   • (b) $4m/s^2$
   • (c) $6m/s^2$
   • (d) $8m/s^2$

2. A $5kg$ block accelerates at $\overrightarrow{a}=3\hat{i}+2\hat{j}m/s^2$. Find the magnitude of the net force.

   • (a) $15N$
   • (b) $17.5N$
   • (c) $20N$
   • (d) $25N$

3. A $10kg$ block on a frictionless incline at ${30}^{\circ }$ ($g=9.8m/s^2$) slides down. Calculate the acceleration.

   • (a) $4.0m/s^2$
   • (b) $4.9m/s^2$
   • (c) $5.6m/s^2$
   • (d) $6.3m/s^2$

4. Two masses $m_1=6kg$ and $m_2=2kg$ are connected in an Atwood’s machine ($g=9.8m/s^2$). Find the acceleration.

   • (a) $2.45m/s^2$
   • (b) $3.0m/s^2$
   • (c) $3.5m/s^2$
   • (d) $4.0m/s^2$

5. A $3kg$ block on a horizontal surface with friction coefficient $\mu =0.3$ ($g=9.8m/s^2$) is pushed by $F=15N$. Calculate the acceleration.

   • (a) $0.5m/s^2$
   • (b) $1.0m/s^2$
   • (c) $1.5m/s^2$
   • (d) $2.0m/s^2$

6. A $2kg$ block in a car accelerating at ${\overrightarrow{a}}_{\text{car}}=4\hat{i}m/s^2$ is observed. Calculate the magnitude of the pseudo-force in the car’s frame.

   • (a) $4N$
   • (b) $6N$
   • (c) $8N$
   • (d) $10N$

7. A person of mass $60kg$ in an elevator accelerating upward at $3m/s^2$ ($g=9.8m/s^2$). Find the apparent weight.

   • (a) $588N$
   • (b) $668N$
   • (c) $768N$
   • (d) $868N$

8. Two blocks A ($3kg$) and B ($5kg$) in contact on a frictionless surface are pushed by $F=24N$ on A. Find the contact force between A and B.

   • (a) $9N$
   • (b) $12N$
   • (c) $15N$
   • (d) $18N$

9. A rocket of mass $2000kg$ accelerates upward at $6m/s^2$ ($g=9.8m/s^2$). Calculate the thrust force.

   • (a) $19600N$
   • (b) $25600N$
   • (c) $31600N$
   • (d) $37600N$

10. A $8kg$ block on a frictionless surface is pulled by $F=40N$ at ${37}^{\circ }$ above the horizontal. Find the horizontal acceleration.

    • (a) $3m/s^2$
    • (b) $4m/s^2$
    • (c) $5m/s^2$
    • (d) $6m/s^2$

11. A $12kg$ block on a frictionless incline at ${45}^{\circ }$ ($g=9.8m/s^2$) is pushed by $F=60N$ parallel to the incline. Calculate the acceleration.

    • (a) $8.0m/s^2$
    • (b) $9.0m/s^2$
    • (c) $10.0m/s^2$
    • (d) $11.0m/s^2$

12. Two masses $m_1=8kg$ and $m_2=4kg$ in an Atwood’s machine ($g=9.8m/s^2$). Find the tension in the string.

    • (a) $47.04N$
    • (b) $52.27N$
    • (c) $58.80N$
    • (d) $64.00N$

13. A $7kg$ block on a surface with $\mu =0.2$ ($g=9.8m/s^2$) is pulled by $F=30N$ horizontally. Calculate the acceleration.

    • (a) $1.6m/s^2$
    • (b) $2.0m/s^2$
    • (c) $2.4m/s^2$
    • (d) $2.8m/s^2$

14. A $1kg$ block in a frame accelerating at ${\overrightarrow{a}}_{\text{frame}}=5\hat{i}+2\hat{j}m/s^2$ is observed. Find the magnitude of the pseudo-force.

    • (a) $3N$
    • (b) $4N$
    • (c) $5.39N$
    • (d) $6.0N$

15. A person of mass $50kg$ in an elevator accelerating downward at $2m/s^2$ ($g=9.8m/s^2$). Find the apparent weight.

    • (a) $390N$
    • (b) $490N$
    • (c) $590N$
    • (d) $690N$

16. A $4kg$ block on a frictionless surface is pushed by $F=20N$ horizontally. Find the acceleration.

    • (a) $2.5m/s^2$
    • (b) $5.0m/s^2$
    • (c) $7.5m/s^2$
    • (d) $10.0m/s^2$

17. Two blocks A ($2kg$) and B ($4kg$) in contact on a frictionless surface are pushed by $F=18N$ on A. Find the contact force.

    • (a) $6N$
    • (b) $9N$
    • (c) $12N$
    • (d) $15N$

18. A $15kg$ block on a frictionless incline at ${60}^{\circ }$ ($g=9.8m/s^2$). Calculate the acceleration down the incline.

    • (a) $7.0m/s^2$
    • (b) $8.0m/s^2$
    • (c) $8.5m/s^2$
    • (d) $9.0m/s^2$

19. A $6kg$ block on a surface with $\mu =0.4$ ($g=9.8m/s^2$) is pulled by $F=40N$. Find the acceleration.

    • (a) $1.5m/s^2$
    • (b) $2.0m/s^2$
    • (c) $2.5m/s^2$
    • (d) $3.0m/s^2$

20. A rocket of mass $3000kg$ accelerates upward at $4m/s^2$ ($g=9.8m/s^2$). Find the thrust force.

    • (a) $29400N$
    • (b) $32400N$
    • (c) $35400N$
    • (d) $41400N$

21. A $5kg$ block in a car accelerating at ${\overrightarrow{a}}_{\text{car}}=3\hat{i}-2\hat{j}m/s^2$. Find the magnitude of the pseudo-force.

    • (a) $10N$
    • (b) $12N$
    • (c) $15N$
    • (d) $18N$

22. A person of mass $70kg$ in an elevator accelerating upward at $1.5m/s^2$ ($g=9.8m/s^2$). Find the apparent weight.

    • (a) $686N$
    • (b) $791N$
    • (c) $896N$
    • (d) $1001N$

23. Two masses $m_1=10kg$ and $m_2=5kg$ in an Atwood’s machine ($g=9.8m/s^2$). Find the acceleration.

    • (a) $2.0m/s^2$
    • (b) $2.5m/s^2$
    • (c) $3.0m/s^2$
    • (d) $3.27m/s^2$

24. A $9kg$ block on a frictionless surface is pulled by $F=36N$ at ${53}^{\circ }$ above the horizontal. Find the horizontal acceleration.

    • (a) $2.0m/s^2$
    • (b) $2.4m/s^2$
    • (c) $3.0m/s^2$
    • (d) $3.6m/s^2$

25. A $20kg$ block on a frictionless incline at ${37}^{\circ }$ ($g=9.8m/s^2$). Calculate the normal force.

    • (a) $120N$
    • (b) $150N$
    • (c) $157.2N$
    • (d) $180N$

26. A $2kg$ block on a surface with $\mu =0.1$ ($g=9.8m/s^2$) is pushed by $F=10N$. Find the acceleration.

    • (a) $3.0m/s^2$
    • (b) $4.0m/s^2$
    • (c) $5.0m/s^2$
    • (d) $6.0m/s^2$

27. A person of mass $80kg$ in an elevator accelerating downward at $1m/s^2$ ($g=9.8m/s^2$). Find the apparent weight.

    • (a) $704N$
    • (b) $784N$
    • (c) $864N$
    • (d) $944N$

28. Two blocks A ($4kg$) and B ($6kg$) in contact on a frictionless surface are pushed by $F=30N$ on A. Find the contact force.

    • (a) $12N$
    • (b) $15N$
    • (c) $18N$
    • (d) $21N$

29. A rocket of mass $1500kg$ accelerates upward at $8m/s^2$ ($g=9.8m/s^2$). Find the thrust force.

    • (a) $14700N$
    • (b) $21700N$
    • (c) $26700N$
    • (d) $31700N$

30. A $6kg$ block on a frictionless surface is pulled by $F=24N$ horizontally. Find the acceleration.

    • (a) $2.0m/s^2$
    • (b) $3.0m/s^2$
    • (c) $4.0m/s^2$
    • (d) $5.0m/s^2$

31. Two masses $m_1=12kg$ and $m_2=8kg$ in an Atwood’s machine ($g=9.8m/s^2$). Find the tension.

    • (a) $94.08N$
    • (b) $104.53N$
    • (c) $117.60N$
    • (d) $128.00N$

32. A $5kg$ block on a surface with $\mu =0.25$ ($g=9.8m/s^2$) is pushed by $F=25N$. Find the acceleration.

    • (a) $1.0m/s^2$
    • (b) $1.5m/s^2$
    • (c) $2.0m/s^2$
    • (d) $2.5m/s^2$

33. A $3kg$ block in a frame accelerating at ${\overrightarrow{a}}_{\text{frame}}=2\hat{i}+3\hat{j}m/s^2$. Find the magnitude of the pseudo-force.

    • (a) $6.0N$
    • (b) $7.5N$
    • (c) $9.0N$
    • (d) $10.5N$

34. A person of mass $40kg$ in an elevator accelerating upward at $2.5m/s^2$ ($g=9.8m/s^2$). Find the apparent weight.

    • (a) $392N$
    • (b) $492N$
    • (c) $592N$
    • (d) $692N$

35. A $7kg$ block on a frictionless incline at ${53}^{\circ }$ ($g=9.8m/s^2$) is pushed by $F=35N$ parallel to the incline. Find the acceleration.

    • (a) $7.0m/s^2$
    • (b) $8.0m/s^2$
    • (c) $9.0m/s^2$
    • (d) $10.0m/s^2$

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Conceptual Problems

36. What does Newton’s first law describe?

• (a) Acceleration due to net force
• (b) Action-reaction pairs
• (c) Inertia and constant velocity when net force is zero
• (d) Pseudo-forces in non-inertial frames

37. What is the net force on an object moving at constant velocity?

• (a) Zero
• (b) Equal to its weight
• (c) Proportional to its mass
• (d) Proportional to its velocity

38. What does Newton’s second law relate?

• (a) Force and velocity
• (b) Force and mass
• (c) Net force and acceleration
• (d) Force and inertia

39. What is true about action-reaction forces in Newton’s third law?

• (a) They act on the same object
• (b) They act on different objects
• (c) They are unequal in magnitude
• (d) They act in the same direction

40. What is the unit of force in SI units?

• (a) $kg$
• (b) $m/s^2$
• (c) $N$
• (d) $J$

41. What does a pseudo-force represent?

• (a) A real force in an inertial frame
• (b) A fictitious force in a non-inertial frame
• (c) A force due to gravity
• (d) A force due to friction

42. What happens to the apparent weight in an elevator accelerating upward?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

43. What is the role of the normal force on an object on a surface?

• (a) Causes motion
• (b) Opposes motion
• (c) Balances forces perpendicular to the surface
• (d) Balances forces parallel to the surface

44. How does friction affect the motion of a block being pushed?

• (a) Increases acceleration
• (b) Decreases acceleration
• (c) Does not affect acceleration
• (d) Causes constant velocity

45. What is the dimension of force?

• (a) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$

46. What does a zero net force imply?

• (a) Object is accelerating
• (b) Object is at rest or moving with constant velocity
• (c) Object is in circular motion
• (d) Object is in a non-inertial frame

47. What is the significance of ${\overrightarrow{F}}_{A\text{ on }B}=-{\overrightarrow{F}}_{B\text{ on }A}$?

• (a) Forces cancel each other
• (b) Forces act on the same object
• (c) Forces are action-reaction pairs
• (d) Forces are perpendicular

48. What is the physical significance of tension in a pulley system?

• (a) Opposes motion
• (b) Transmits force along the string
• (c) Causes friction
• (d) Changes direction of motion

49. What does an inertial frame imply?

• (a) Frame is accelerating
• (b) Newton’s laws hold directly
• (c) Pseudo-forces are required
• (d) Frame is rotating

50. How does mass affect acceleration for a given force?

• (a) Acceleration is directly proportional to mass
• (b) Acceleration is inversely proportional to mass
• (c) Acceleration is independent of mass
• (d) Acceleration equals mass

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Derivation Problems

51. Derive the condition for constant velocity using Newton’s first law.

52. Derive the expression for acceleration using Newton’s second law for a single force.

53. Derive the unit of force (newton) using Newton’s second law.

54. Derive the acceleration of a block on a frictionless incline.

55. Derive the tension in an Atwood’s machine with two masses.

56. Derive the pseudo-force in a non-inertial frame accelerating at ${\overrightarrow{a}}_{\text{frame}}$.

57. Derive the apparent weight in an elevator accelerating upward.

58. Derive the contact force between two blocks pushed together on a frictionless surface.

59. Derive the acceleration of a block with friction being pushed horizontally.

60. Derive the thrust force of a rocket accelerating upward.

61. Derive the acceleration of a block pulled at an angle on a frictionless surface.

62. Derive the normal force on a block on an incline.

63. Derive the net force required for a given acceleration in 2D.

64. Derive the acceleration in a non-inertial frame with a single applied force.

65. Derive the relationship between action-reaction forces in a two-body system.

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NEET-style Conceptual Problems

66. What is the unit of mass in SI units?

• (a) $kg$
• (b) $N$
• (c) $m/s^2$
• (d) $J$

67. What does a zero acceleration imply in Newton’s first law?

• (a) Net force is zero
• (b) Net force is non-zero
• (c) Object is accelerating
• (d) Object is in a non-inertial frame

68. Which quantity is a vector in dynamics?

• (a) Mass
• (b) Force
• (c) Speed
• (d) Time

69. What is the direction of the pseudo-force in a non-inertial frame?

• (a) Same as the frame’s acceleration
• (b) Opposite to the frame’s acceleration
• (c) Perpendicular to the frame’s acceleration
• (d) Along the velocity

70. What is the dimension of acceleration?

• (a) $[\text{L}{\text{T}}^{-1}]$
• (b) $[\text{L}{\text{T}}^{-2}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (d) $[{\text{L}}^2{\text{T}}^{-2}]$

71. What does inertia represent?

• (a) Resistance to change in motion
• (b) Acceleration due to force
• (c) Action-reaction pair
• (d) Pseudo-force

72. What is the role of the normal force in dynamics?

• (a) Causes motion
• (b) Opposes motion
• (c) Balances forces perpendicular to the surface
• (d) Balances forces parallel to the surface

73. What happens to the apparent weight in an elevator accelerating downward?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

74. Why do action-reaction forces not cancel each other?

• (a) They act on the same object
• (b) They act on different objects
• (c) They are unequal in magnitude
• (d) They act in the same direction

75. What is the unit of tension in SI units?

• (a) $kg$
• (b) $N$
• (c) $m/s^2$
• (d) $J$

76. What does a constant velocity imply?

• (a) Zero net force
• (b) Constant net force
• (c) Zero acceleration
• (d) Both (a) and (c)

77. Which law explains the force between two blocks in contact?

• (a) Newton’s first law
• (b) Newton’s second law
• (c) Newton’s third law
• (d) Law of gravitation

78. What is the direction of friction on a block being pushed?

• (a) Same as the applied force
• (b) Opposite to the applied force
• (c) Perpendicular to the applied force
• (d) Along the normal force

79. What does an inertial frame imply?

• (a) Frame is accelerating
• (b) Newton’s laws hold directly
• (c) Pseudo-forces are required
• (d) Frame is rotating

80. What does Newton’s second law relate?

• (a) Force and velocity
• (b) Force and mass
• (c) Net force and acceleration
• (d) Force and inertia

81. What is the dimension of the pseudo-force?

• (a) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$

82. What is the role of tension in a pulley system?

• (a) Opposes motion
• (b) Transmits force along the string
• (c) Causes friction
• (d) Changes direction of motion

83. What happens to acceleration if mass doubles for a constant force?

• (a) Doubles
• (b) Halves
• (c) Remains the same
• (d) Becomes zero

84. Which quantity is a scalar in dynamics?

• (a) Force
• (b) Acceleration
• (c) Mass
• (d) Velocity

85. What does a negative pseudo-force component indicate?

• (a) Frame accelerating in the same direction
• (b) Frame accelerating in the opposite direction
• (c) Frame at rest
• (d) Frame rotating

86. What is the unit of apparent weight?

• (a) $kg$
• (b) $N$
• (c) $m/s^2$
• (d) $J$

87. What does Newton’s third law explain in a rocket’s motion?

• (a) Inertia of the rocket
• (b) Acceleration due to thrust
• (c) Action-reaction between exhaust and rocket
• (d) Friction on the rocket

88. Why does friction oppose motion?

• (a) It acts in the direction of motion
• (b) It acts opposite to the direction of motion
• (c) It acts perpendicular to motion
• (d) It acts along the normal force

89. What is the significance of $\overrightarrow{F}=m\overrightarrow{a}$?

• (a) Defines inertia
• (b) Relates net force to acceleration
• (c) Describes action-reaction
• (d) Defines pseudo-forces

90. How does the normal force affect motion on an incline?

• (a) Causes motion down the incline
• (b) Prevents motion through the incline
• (c) Opposes motion down the incline
• (d) Increases acceleration

91. What is the role of Newton’s first law in dynamics?

• (a) Defines force
• (b) Defines acceleration
• (c) Defines inertia
• (d) Defines action-reaction

92. What does a zero net force indicate?

• (a) Object is accelerating
• (b) Object is at rest or moving with constant velocity
• (c) Object is in circular motion
• (d) Object is in a non-inertial frame

93. What is the physical significance of ${\overrightarrow{F}}_{B\text{ on }A}$?

• (a) Force on B by A
• (b) Force on A by B
• (c) Net force on A
• (d) Net force on B

94. What is the dimension of tension?

• (a) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$

95. Why does the apparent weight change in an elevator?

• (a) Due to constant velocity
• (b) Due to acceleration of the frame
• (c) Due to friction
• (d) Due to gravity changing

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NEET-style Numerical Problems

96. A $5kg$ block on a frictionless surface is pushed by $F=25N$ horizontally. What is the acceleration?

• (a) $2.0m/s^2$
• (b) $3.0m/s^2$
• (c) $4.0m/s^2$
• (d) $5.0m/s^2$

97. A person of mass $60kg$ in an elevator accelerating upward at $2m/s^2$ ($g=9.8m/s^2$). What is the apparent weight?

• (a) $588N$
• (b) $688N$
• (c) $708N$
• (d) $808N$

98. Two masses $m_1=8kg$ and $m_2=2kg$ in an Atwood’s machine ($g=9.8m/s^2$). What is the acceleration?

• (a) $2.0m/s^2$
• (b) $2.5m/s^2$
• (c) $3.0m/s^2$
• (d) $3.5m/s^2$

99. A $4kg$ block on a surface with $\mu =0.2$ ($g=9.8m/s^2$) is pushed by $F=20N$. What is the acceleration?

• (a) $1.5m/s^2$
• (b) $2.0m/s^2$
• (c) $2.5m/s^2$
• (d) $3.0m/s^2$

100. A $2kg$ block in a car accelerating at ${\overrightarrow{a}}_{\text{car}}=3\hat{i}+4\hat{j}m/s^2$. What is the magnitude of the pseudo-force?
     - (a) $5N$
     - (b) $10N$
     - (c) $15N$
     - (d) $20N$

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