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NCERT Solutions › Physics › Chapter 7

Chapter 7: System of Particles

NCERT Solutions for CBSE Class 10 Physics — 105 solved questions with detailed explanations.

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Solved Questions

Q1. The angular momentum of a particle moving in a circle of radius r with speed v and mass m is:

Difficulty: Easy · Topic: Angular Momentum

Solution

Angular momentum L = mvr for a particle in circular motion, where v is tangential velocity.

Q2. The moment of inertia of a thin uniform rod of mass M and length L about an axis perpendicular to the rod through its centre is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

For a thin rod about centre: I = ML²/12. About end: I = ML²/3.

Q3. The moment of inertia of a thin rod about centre is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of thin rod about centre = ML²/12.

Q4. The moment of inertia of a thin rod about end is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of thin rod about end = ML²/3.

Q5. The moment of inertia of a solid sphere about diameter is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of solid sphere about diameter = 2MR²/5.

Q6. The moment of inertia of a hollow sphere about diameter is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of hollow sphere about diameter = 2MR²/3.

Q7. The moment of inertia of a solid cylinder about axis is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of solid cylinder about axis = MR²/2.

Q8. The moment of inertia of a thin ring about axis is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of thin ring about axis = MR².

Q9. The moment of inertia of a solid disc about diameter is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of solid disc about diameter = MR²/4.

Q10. The moment of inertia of a solid cylinder about diameter is:

Difficulty: Easy-Medium · Topic: Moment of Inertia

Solution

Standard result: MI of solid cylinder about diameter = M(R²/4 + L²/12).

Q11. Two particles of masses 1 kg and 3 kg are separated by 4 m. The COM from the 1 kg mass is:

Difficulty: Easy-Medium · Topic: Centre of Mass

Solution

x_cm = m₂d/(m₁+m₂) = 3×4/4 = 3.0 m.

Q12. Two particles of masses 2 kg and 6 kg are separated by 8 m. The COM from the 2 kg mass is:

Difficulty: Easy-Medium · Topic: Centre of Mass

Solution

x_cm = m₂d/(m₁+m₂) = 6×8/8 = 6.0 m.

Q13. Two particles of masses 3 kg and 5 kg are separated by 16 m. The COM from the 3 kg mass is:

Difficulty: Easy-Medium · Topic: Centre of Mass

Solution

x_cm = m₂d/(m₁+m₂) = 5×16/8 = 10.0 m.

Q14. Two particles of masses 1 kg and 1 kg are separated by 10 m. The COM from the 1 kg mass is:

Difficulty: Easy-Medium · Topic: Centre of Mass

Solution

x_cm = m₂d/(m₁+m₂) = 1×10/2 = 5.0 m.

Q15. Two particles of masses 4 kg and 6 kg are separated by 5 m. The COM from the 4 kg mass is:

Difficulty: Easy-Medium · Topic: Centre of Mass

Solution

x_cm = m₂d/(m₁+m₂) = 6×5/10 = 3.0 m.

Q16. A disc of mass 2 kg and radius 0.2 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×2×0.2².

Q17. A disc of mass 3 kg and radius 0.3 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×3×0.3².

Q18. A disc of mass 4 kg and radius 0.4 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×4×0.4².

Q19. A disc of mass 5 kg and radius 0.5 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×5×0.5².

Q20. A disc of mass 6 kg and radius 0.6 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×6×0.6².

Q21. A disc of mass 7 kg and radius 0.7 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×7×0.7².

Q22. A disc of mass 8 kg and radius 0.8 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×8×0.8².

Q23. A disc of mass 9 kg and radius 0.9 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×9×0.9².

Q24. A disc of mass 10 kg and radius 1.0 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×10×1.0².

Q25. A disc of mass 11 kg and radius 1.1 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×11×1.1².

Q26. A disc of mass 12 kg and radius 1.2 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×12×1.2².

Q27. A disc of mass 13 kg and radius 1.3 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×13×1.3².

Q28. A disc of mass 14 kg and radius 1.4 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×14×1.4².

Q29. A disc of mass 15 kg and radius 1.5 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×15×1.5².

Q30. A disc of mass 16 kg and radius 1.6 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×16×1.6².

Q31. A disc of mass 17 kg and radius 1.7 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×17×1.7².

Q32. A disc of mass 18 kg and radius 1.8 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×18×1.8².

Q33. A disc of mass 19 kg and radius 1.9 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×19×1.9².

Q34. A disc of mass 20 kg and radius 2.0 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×20×2.0².

Q35. A disc of mass 21 kg and radius 2.1 m has moment of inertia about its axis:

Difficulty: Easy-Medium · Topic: MI Calculation

Solution

I = ½MR² = 0.5×21×2.1².

Q36. Masses 1kg and 1kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*2/2=1.0 m.

Q37. Masses 1kg and 1kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*4/2=2.0 m.

Q38. Masses 1kg and 1kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*6/2=3.0 m.

Q39. Masses 1kg and 1kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*8/2=4.0 m.

Q40. Masses 1kg and 1kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*10/2=5.0 m.

Q41. Masses 1kg and 1kg separated by 12m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*12/2=6.0 m.

Q42. Masses 1kg and 1kg separated by 14m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*14/2=7.0 m.

Q43. Masses 1kg and 1kg separated by 16m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*16/2=8.0 m.

Q44. Masses 1kg and 1kg separated by 18m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=1*18/2=9.0 m.

Q45. Masses 1kg and 2kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*2/3=1.33 m.

Q46. Masses 1kg and 2kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*4/3=2.67 m.

Q47. Masses 1kg and 2kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*6/3=4.0 m.

Q48. Masses 1kg and 2kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*8/3=5.33 m.

Q49. Masses 1kg and 2kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*10/3=6.67 m.

Q50. Masses 1kg and 2kg separated by 12m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*12/3=8.0 m.

Q51. Masses 1kg and 2kg separated by 14m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*14/3=9.33 m.

Q52. Masses 1kg and 2kg separated by 16m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*16/3=10.67 m.

Q53. Masses 1kg and 2kg separated by 18m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=2*18/3=12.0 m.

Q54. Masses 1kg and 3kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*2/4=1.5 m.

Q55. Masses 1kg and 3kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*4/4=3.0 m.

Q56. Masses 1kg and 3kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*6/4=4.5 m.

Q57. Masses 1kg and 3kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*8/4=6.0 m.

Q58. Masses 1kg and 3kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*10/4=7.5 m.

Q59. Masses 1kg and 3kg separated by 12m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*12/4=9.0 m.

Q60. Masses 1kg and 3kg separated by 14m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*14/4=10.5 m.

Q61. Masses 1kg and 3kg separated by 16m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*16/4=12.0 m.

Q62. Masses 1kg and 3kg separated by 18m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=3*18/4=13.5 m.

Q63. Masses 1kg and 4kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*2/5=1.6 m.

Q64. Masses 1kg and 4kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*4/5=3.2 m.

Q65. Masses 1kg and 4kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*6/5=4.8 m.

Q66. Masses 1kg and 4kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*8/5=6.4 m.

Q67. Masses 1kg and 4kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*10/5=8.0 m.

Q68. Masses 1kg and 4kg separated by 12m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*12/5=9.6 m.

Q69. Masses 1kg and 4kg separated by 14m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*14/5=11.2 m.

Q70. Masses 1kg and 4kg separated by 16m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*16/5=12.8 m.

Q71. Masses 1kg and 4kg separated by 18m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=4*18/5=14.4 m.

Q72. Masses 1kg and 5kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*2/6=1.67 m.

Q73. Masses 1kg and 5kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*4/6=3.33 m.

Q74. Masses 1kg and 5kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*6/6=5.0 m.

Q75. Masses 1kg and 5kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*8/6=6.67 m.

Q76. Masses 1kg and 5kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*10/6=8.33 m.

Q77. Masses 1kg and 5kg separated by 12m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*12/6=10.0 m.

Q78. Masses 1kg and 5kg separated by 14m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*14/6=11.67 m.

Q79. Masses 1kg and 5kg separated by 16m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*16/6=13.33 m.

Q80. Masses 1kg and 5kg separated by 18m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=5*18/6=15.0 m.

Q81. Masses 1kg and 6kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*2/7=1.71 m.

Q82. Masses 1kg and 6kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*4/7=3.43 m.

Q83. Masses 1kg and 6kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*6/7=5.14 m.

Q84. Masses 1kg and 6kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*8/7=6.86 m.

Q85. Masses 1kg and 6kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*10/7=8.57 m.

Q86. Masses 1kg and 6kg separated by 12m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*12/7=10.29 m.

Q87. Masses 1kg and 6kg separated by 14m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*14/7=12.0 m.

Q88. Masses 1kg and 6kg separated by 16m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*16/7=13.71 m.

Q89. Masses 1kg and 6kg separated by 18m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=6*18/7=15.43 m.

Q90. Masses 1kg and 7kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*2/8=1.75 m.

Q91. Masses 1kg and 7kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*4/8=3.5 m.

Q92. Masses 1kg and 7kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*6/8=5.25 m.

Q93. Masses 1kg and 7kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*8/8=7.0 m.

Q94. Masses 1kg and 7kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*10/8=8.75 m.

Q95. Masses 1kg and 7kg separated by 12m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*12/8=10.5 m.

Q96. Masses 1kg and 7kg separated by 14m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*14/8=12.25 m.

Q97. Masses 1kg and 7kg separated by 16m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*16/8=14.0 m.

Q98. Masses 1kg and 7kg separated by 18m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=7*18/8=15.75 m.

Q99. Masses 1kg and 8kg separated by 2m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=8*2/9=1.78 m.

Q100. Masses 1kg and 8kg separated by 4m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=8*4/9=3.56 m.

Q101. Masses 1kg and 8kg separated by 6m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=8*6/9=5.33 m.

Q102. Masses 1kg and 8kg separated by 8m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=8*8/9=7.11 m.

Q103. Masses 1kg and 8kg separated by 10m. COM from m1:

Difficulty: Easy-Medium · Topic: COM

Solution

x=m2*d/(m1+m2)=8*10/9=8.89 m.

Q104. The centre of mass of a uniform semicircular ring of radius R lies at a distance from the centre equal to:

Difficulty: Medium · Topic: Centre of Mass

Solution

For a uniform semicircular ring, y_cm = 2R/π from the centre along the axis of symmetry.

Q105. A disc and a sphere of same mass and radius roll down an inclined plane. Which reaches the bottom first?

Difficulty: Medium · Topic: Rolling Motion

Solution

Acceleration a = gsinθ/(1+I/MR²). For sphere I/MR² = 2/5, for disc = 1/2. Since 2/5 < 1/2, sphere has higher acceleration and reaches first.

Other Chapters in Physics

Ch 1: Physical WorldCh 2: Units & MeasurementsCh 3: Motion in a Straight LineCh 4: Motion in a PlaneCh 5: Laws of MotionCh 6: Work Energy & PowerCh 8: GravitationCh 9: Mechanical Properties of SolidsCh 10: Mechanical Properties of FluidsCh 11: Thermal Properties of MatterCh 12: ThermodynamicsCh 13: Kinetic TheoryCh 14: OscillationsCh 15: Waves

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