NEET UG - Moment of inertia, radius of gyration, moments of inertia for simple geometrical objects One Line Questions & Answers

1. If the radius of gyration of a body about an axis is K and the distance of the center of mass from the axis is d, then the radius of gyration about a parallel axis through the center of mass is given by: — √(K^2 - d^2)

2. For a rigid body, the moment of inertia is the sum of the products of each elemental mass and the square of its perpendicular distance from the axis of rotation. This is represented by which integral? — ∫ r^2 dm

3. The moment of inertia of a thin spherical shell of mass M and radius R about an axis passing through its center is: — MR^2

4. The moment of inertia of a solid sphere of mass M and radius R about an axis tangential to the sphere and passing through a point on the surface is: — 9/5 MR^2

5. The Perpendicular Axis Theorem is applicable to planar bodies, such as discs and rings. It relates the moments of inertia about axes in which orientation? — Perpendicular to the plane and two perpendicular axes in the plane

6. The Perpendicular Axis Theorem states that I_z = I_x + I_y. For this theorem to be valid, which of the following must be true about the axes x, y, and z? — Axes x and y are in the plane, and axis z is perpendicular to the plane

7. If I_cm is the moment of inertia about an axis through the center of mass and I is the moment of inertia about a parallel axis at a distance 'd', what is the relation according to the Parallel Axis Theorem? — I = I_cm + Md^2

8. For a planar body, if I_x and I_y are the moments of inertia about two perpendicular axes in the plane, and I_z is the moment of inertia about an axis perpendicular to the plane passing through the intersection of x and y axes, then: — I_z = I_x + I_y

9. Which statement about moment of inertia is incorrect? — It is independent of the mass distribution.

10. What is the SI unit of moment of inertia? — kg m^2

11. What is the radius of gyration of a thin uniform rod of mass M and length L about an axis passing through one of its ends and perpendicular to its length? — L/√3

12. What is the radius of gyration of a thin uniform rod of mass M and length L about an axis passing through its center and perpendicular to its length? — L/√12

13. If a body's mass is concentrated at a single point at distance r from the axis, its moment of inertia is given by: — mr^2

14. Consider a system of four identical particles of mass m placed at the corners of a square of side 'a'. What is the moment of inertia about an axis passing through the center of the square and perpendicular to its plane? — 2ma^2

15. The moment of inertia of a body depends on which of the following factors? — Mass distribution and axis of rotation

16. Which of the following factors is NOT considered when calculating the moment of inertia of a rigid body? — Linear velocity of the body

17. The radius of gyration (K) of a body is defined such that its moment of inertia is equal to: — MK^2

18. If a body has mass M and radius of gyration K, what is the moment of inertia of the body about a given axis? — MK^2

19. For a thin uniform rod of mass M and length L, the moment of inertia about an axis perpendicular to the rod and passing through a point at distance L/3 from the center is: — ML^2/4

20. The moment of inertia of a thin uniform rod of mass M and length L about an axis perpendicular to the rod at one end is ML^2/3. Using the Parallel Axis Theorem, find the moment of inertia about an axis parallel to this, passing through the center of the rod. — ML^2/12

21. Consider a system of two identical particles of mass m separated by a distance L. What is the moment of inertia of this system about an axis passing through the midpoint of the line joining the particles and perpendicular to it? — mL^2/4

22. What is the moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its center and perpendicular to its length? — ML^2/12

23. What is the moment of inertia of a thin uniform rod of mass M and length L about an axis passing through one of its ends and perpendicular to its length? — ML^2/3

24. What is the moment of inertia of a point mass 'm' at a distance 'r' from the axis of rotation? — mr^2

25. What is the moment of inertia of a thin uniform circular ring of mass M and radius R about a diameter? — MR^2/2

26. What is the moment of inertia of a thin uniform disc of mass M and radius R about an axis passing through its center and perpendicular to its plane? — MR^2/2

27. What is the moment of inertia of a thin uniform disc of mass M and radius R about a diameter? — MR^2/2

28. What is the moment of inertia of a solid sphere of mass M and radius R about an axis passing through its center? — 2MR^2/5

29. What is the moment of inertia of a hollow sphere of mass M and radius R about an axis passing through its center? — MR^2

30. What is the moment of inertia of a solid cylinder of mass M and radius R about its longitudinal axis (axis passing through the center and along its length)? — MR^2/2

31. If the radius of gyration of a hollow sphere of mass M and radius R about an axis through its center is R, what is its moment of inertia about the same axis? — MR^2

32. What is the moment of inertia of a thin uniform circular ring of mass M and radius R about an axis passing through its center and perpendicular to its plane? — MR^2

33. What is the moment of inertia of a hollow cylinder (thin tube) of mass M and radius R about its longitudinal axis? — MR^2

34. The moment of inertia of a thin uniform disc of mass M and radius R about an axis tangential to the disc and lying in its plane is: — 5/4 MR^2

35. Consider a thin uniform rod of mass M and length L. If we want to find its moment of inertia about an axis perpendicular to the rod at a distance x from one end, which theorem would be most useful after knowing I_cm? — Parallel Axis Theorem

36. What is the radius of gyration of a thin uniform circular ring of mass M and radius R about an axis passing through its center and perpendicular to its plane? — R

37. What is the radius of gyration of a thin uniform disc of mass M and radius R about an axis passing through its center and perpendicular to its plane? — R/√2

38. What is the radius of gyration of a solid sphere of mass M and radius R about an axis passing through its center? — √(2/5) R

39. What is the radius of gyration of a hollow sphere of mass M and radius R about an axis passing through its center? — R

40. What is the radius of gyration of a solid cylinder of mass M and radius R about its longitudinal axis? — R/√2

41. What is the radius of gyration of a hollow cylinder (thin tube) of mass M and radius R about its longitudinal axis? — R

42. The radius of gyration of a thin uniform disc of mass M and radius R about a diameter is: — R/2

43. The moment of inertia is also known as: — Rotational inertia

44. Which of the following has the largest moment of inertia for the same mass and radius, about an axis through its center and perpendicular to its plane? — Thin ring

45. If a body is composed of several particles, its total moment of inertia about an axis is the sum of the moments of inertia of individual particles about the same axis. This is due to the principle of: — Superposition

46. For a given mass distribution, the radius of gyration is minimum when the axis of rotation passes through: — The center of mass

47. The Parallel Axis Theorem states that the moment of inertia of a body about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus: — The product of mass and the square of the distance between the axes

48. Which of the following has the smallest moment of inertia for the same mass and radius, about an axis through its center and perpendicular to its plane (for planar objects) or through its center (for spherical objects)? — Solid sphere

49. The moment of inertia of a body is analogous to which quantity in linear motion? — Mass

Moment of inertia, radius of gyration, moments of inertia for simple geometrical objects - One Line Questions