Free NEET Physics multiple-choice questions on Moment of Inertia & Theorems. Attempt each question and reveal the answer with a full explanation.
Which of the following physical quantities is the rotational analogue of mass? Moment of Inertia Torque Angular Momentum Angular Acceleration A uniform rectangular plate of mass M and sides a and b is rotating about an axis passing through its center and perpendicular to its plane. The moment of inertia is: M(a 2 + b 2) 12 M(a 2 + b 2) 3 Ma 2 12 Mb 2 12 The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc is: 3 2 MR 2 1 2 MR 2 MR 2 2 5 MR 2 What is the moment of inertia of a solid sphere of mass M and radius R about a tangent to the sphere? 7 5 MR 2 2 5 MR 2 3 5 MR 2 5 2 MR 2 A flywheel is a uniform disc of mass 72 kg and radius 0.5 m . When it is rotating at 10 rev/s , its rotational kinetic energy is: 1800 2 J 900 2 J 3600 2 J 450 2 J A uniform thin rod of mass M and length L is bent into a circle. The moment of inertia of the circle about an axis passing through its center and perpendicular to its plane is: ML 2 4 2 ML 2 12 ML 2 2 2 ML 2 An L-shaped object is made of two thin uniform rods of mass M and length L each. The moment of inertia of this object about an axis passing through the corner and perpendicular to the plane of the 'L' is: 2 3 ML 2 1 3 ML 2 1 2 ML 2 1 12 ML 2 Four point masses, each of mass m , are fixed at the corners of a square of side a . The moment of inertia of the system about an axis passing through the center of the square and perpendicular to its plane is: 2ma 2 ma 2 4ma 2 1 2 ma 2 For a given mass and radius, which of the following has the smallest moment of inertia about its symmetry axis? Solid sphere Hollow sphere Solid cylinder Hollow cylinder Three objects, a solid sphere, a thin circular disc and a thin circular ring, each have the same mass M and radius R . They all spin with the same angular speed about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation: W ring > W disc > W sphere W sphere > W disc > W ring W ring > W sphere > W disc W disc > W ring > W sphere What is the radius of gyration of a hollow sphere of mass M and radius R about a tangent to the sphere? 5 3 R 2 3 R 7 5 R 3 5 R The moment of inertia of a uniform thin rod of mass M and length L about an axis passing through its center and perpendicular to its length is I . What is its moment of inertia about an axis passing through one of its ends and perpendicular to its length? 4I 3I 2I 3 2 I The ratio of the radius of gyration of a thin uniform disc about an axis passing through its center and normal to its plane to the radius of gyration of the disc about its diameter is: 2 : 1 2 : 1 2 : 3 1 : 2 The ratio of the radius of gyration of a solid sphere of radius R about its own axis to the radius of gyration of the thin hollow sphere of same radius R about its axis is: 3 : 5 3 : 5 2 : 3 2 : 3 The moment of inertia of a uniform circular disc of mass M and radius R about a tangent perpendicular to the plane of the disc is: 3 2 MR 2 1 2 MR 2 5 4 MR 2 MR 2 The radius of gyration of a hollow sphere of mass M and radius R about a diameter is: 2/3 R 2/5 R R/ 2 3/5 R A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ? Disk Sphere Both reach at the same time Depends on their masses A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy ( K t ) as well as rotational kinetic energy ( K r ) simultaneously. The ratio K t : (K t + K r) for the sphere is 10 : 7 5 : 7 7 : 10 2 : 5 A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct ( P and Q are any highest and lowest points on the wheel, respectively)? Point P moves slower than point Q Point P moves faster than point Q Both the points P and Q move with equal speed Point P has zero speed From a circular ring of mass M and radius R , an arc corresponding to a 90 sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the center of the ring and perpendicular to its plane is K times MR 2 . Then the value of K is: 3 4 1 4 1 8 7 8 A thin rod of length L and mass M is bent at its midpoint into the shape of a 'V' with an angle 60 . The moment of inertia of this bent rod about an axis passing through the bending point and perpendicular to the plane of the rod is: ML 2 12 ML 2 24 ML 2 3 ML 2 6 A circular disc is to be made using iron and aluminum so that it has the maximum moment of inertia about its geometric axis. It should be prepared such that: Iron is at the interior and aluminum at the exterior Aluminum is at the interior and iron at the exterior Both are used in alternate layers The density is uniform throughout The ratio of the radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centers and perpendicular to their planes are: 2 : 1 1 : 2 2 : 1 1 : 2 A solid sphere of mass M and radius R is rotating about its diameter. A solid cylinder of the same mass and radius is also rotating about its geometrical axis. If both have the same angular momentum, the ratio of their kinetic energies of rotation ( E sphere / E cylinder ) is: 5/4 4/5 2/5 5/2 The ratio of the radii of gyration of a circular ring to a circular disc, both of same mass and radius, about their respective tangential axes perpendicular to their planes is: 2 : 3 3 : 2 2 : 3 3 : 2 A uniform thin bar of mass M and length L is bent to form a semi-circle. Its moment of inertia about an axis passing through the center of the semi-circle and perpendicular to its plane is: ML 2 2 ML 2 2 2 ML 2 4 2 2ML 2 2 A uniform square plate of side a and mass m has a moment of inertia I about an axis perpendicular to its plane and passing through its center. If a quarter of the plate is removed, the moment of inertia of the remaining part about the same axis is: 3I/4 I/2 I/4 I/3 The moment of inertia of a uniform thin rod of length L and mass M about an axis passing through a point L/4 from one of its ends and perpendicular to the rod is: 7ML 2 48 ML 2 12 ML 2 9 19ML 2 48 A uniform square plate of mass m and side a is rotating about one of its edges. The moment of inertia is: ma 2 3 ma 2 6 ma 2 12 2ma 2 3 A uniform thin rod of mass M and length L is bent into a semi-circle. What is the moment of inertia of the semi-circle about an axis passing through its center of curvature and perpendicular to its plane? ML 2 / 2 ML 2 / 2 2 ML 2 / 4 2 ML 2 / 12 A uniform cylinder has a radius R and length L . If the moment of inertia of this cylinder about its central axis is equal to the moment of inertia about the axis passing through its center and perpendicular to its length, then the ratio L/R is: 3 2 3 2 The moment of inertia of a uniform circular disc of mass M and radius R about a diameter is I . Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be: 6I 4I 5I 3I A light rod of length l has two masses m 1 and m 2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the center of mass is: m 1 m 2 m 1 + m 2 l 2 (m 1 + m 2) l 2 m 1 m 2 l 2 m 1 + m 2 m 1 m 2 l 2 What is the radius of gyration of a uniform rod of length L about an axis perpendicular to its length and passing through its center? L/(2 3 ) L/ 3 L/2 L/ 12 The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its center and making an angle with the rod is: ML 2 12 2 ML 2 12 2 ML 2 3 2 ML 2 12 The radius of gyration of a uniform circular disc of radius R about a tangential axis in the plane of the disc is: 5 4 R 2 3 R R 2 3 2 R A uniform thin rod of mass m and length L is bent at its center into the shape of a 'V' with an angle of 90 . The moment of inertia of the rod about an axis passing through the vertex and perpendicular to the plane of the 'V' is: mL 2 12 mL 2 3 mL 2 6 mL 2 24 A circular disc of mass M and radius R has a concentric hole of radius r . The moment of inertia of this annular disc about an axis passing through its center and perpendicular to its plane is: 1 2 M(R 2 + r 2) 1 2 M(R 2 - r 2) 1 2 M(R 4 - r 4) 1 2 MR 2 A uniform rectangular lamina of mass M and sides a and b has a moment of inertia about an axis passing through one of its corners and perpendicular to its plane given by: M(a 2 + b 2) 3 M(a 2 + b 2) 12 M(a 2 + b 2) 6 M(a 2 + b 2) 4 The moment of inertia of a uniform thin rod of mass M and length L about an axis perpendicular to the rod and passing through a point at distance L/3 from one of its ends is: 1 9 ML 2 1 12 ML 2 7 36 ML 2 1 3 ML 2 The moment of inertia of a uniform circular disc of mass M and radius R about an axis in the plane of the disc and at a distance R/2 from the center is: 1 2 MR 2 3 4 MR 2 1 4 MR 2 5 8 MR 2 A uniform square plate of mass M and side a is rotating about an axis passing through one of its corners and perpendicular to the plate. Its moment of inertia is: 2 3 Ma 2 1 6 Ma 2 1 3 Ma 2 1 12 Ma 2 What is the radius of gyration of a solid cylinder of mass M , length L and radius R about a diameter passing through its center? R 2 4 + L 2 12 R 2 2 + L 2 12 R 2 L 12 A uniform thin rod of length L and mass M is bent into a circle. The moment of inertia of this circle about a diameter is: ML 2 8 2 ML 2 4 2 ML 2 2 2 ML 2 16 2 Which of the following bodies of same mass and radius has the largest moment of inertia about its geometric axis? Hollow cylinder Solid cylinder Solid sphere Hollow sphere What is the moment of inertia of a solid sphere of mass M and radius R about an axis at a distance R/2 from the center? 13 20 MR 2 2 5 MR 2 9 20 MR 2 7 10 MR 2 A thin wire of length L and mass M is bent into a semi-circle. The moment of inertia of the semi-circle about its diameter (the line joining the two ends) is: ML 2 2 2 ML 2 8 2 ML 2 4 2 ML 2 2 The moment of inertia of a square frame consisting of four identical uniform rods, each of mass M and length L , about an axis passing through its center and perpendicular to the plane of the frame is: 4 3 ML 2 2 3 ML 2 1 3 ML 2 1 12 ML 2 What is the moment of inertia of a uniform circular ring of mass M and radius R about a chord at a distance R/2 from the center of the ring? 3 4 MR 2 1 2 MR 2 MR 2 5 4 MR 2 The radius of gyration of a solid cylinder of mass M , radius R and length L about an axis passing through its center and perpendicular to its length is: R 2 4 + L 2 12 R 2 2 + L 2 12 R 2 L 12 A uniform thin rod of length L and mass M is bent at its center into a 'V' shape with an angle 120 . The moment of inertia of this bent rod about an axis passing through the vertex and perpendicular to the plane of the rod is: 1 3 ML 2 1 12 ML 2 1 6 ML 2 1 4 ML 2 The moment of inertia of a uniform semi-circular wire of mass M and radius R about an axis passing through its two ends (the diameter) is: 1 2 MR 2 MR 2 1 4 MR 2 2 3 MR 2 A uniform rectangular plate of mass M and dimensions a b has a moment of inertia I 0 about an axis through its center perpendicular to the plate. If the plate is folded along a line passing through the midpoints of the sides of length a to form a double-layered plate of dimensions a (b/2) , the new moment of inertia about the same axis is: M 12 (a 2 + b 2 4 ) I 0 / 2 I 0 / 4 I 0 What is the moment of inertia of a uniform solid cone of mass M and base radius R about its axis of symmetry? 3 10 MR 2 1 2 MR 2 2 5 MR 2 3 5 MR 2 The radius of gyration of a uniform circular disc of radius R about a tangential axis perpendicular to the plane of the disc is: 3 2 R 5 4 R 3 2 R 2 R What is the moment of inertia of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder? 3 2 MR 2 1 2 MR 2 2 MR 2 5 4 MR 2 A uniform thin rod of length L and mass M is bent at its midpoint to form an angle of 90 . The moment of inertia of this bent rod about an axis passing through the vertex and perpendicular to the plane of the rod is: 1 3 ML 2 1 12 ML 2 1 6 ML 2 1 4 ML 2 The moment of inertia of a square plate of side L and mass M about an axis passing through its center and perpendicular to its plane is I 0 . The moment of inertia of the same plate about an axis passing through one of its vertices and perpendicular to its plane is: 4 I 0 2 I 0 3 I 0 3 2 I 0 A uniform wire of length L and mass M is bent into a circle. The moment of inertia of the circle about an axis tangential to the circle and in its plane is: 3 8 2 ML 2 1 4 2 ML 2 3 4 2 ML 2 1 2 2 ML 2 A solid sphere and a solid cylinder have the same mass and same radius. Which one has the larger radius of gyration about their respective central axes? Solid Cylinder Solid Sphere Both have the same Depends on the density A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle . The frictional force- Decreases the rotational and translational motion Dissipates energy as heat Decreases the rotational motion Converts translational energy to rotational energy A small object of uniform density rolls up a curved surface with an initial velocity v . It reaches up to a maximum height of 3v 2 4g with respect to the initial position. The object is Ring Solid sphere Hollow sphere Disc The ratio of the accelerations for a soldi sphere (mass 'm' and radius 'R') rolling down an incline of angle ' ' without slipping and slipping down the incline without rolling is :- 5 : 7 2 : 3 2 : 5 7 : 5 The rotational kinetic energy of a solid sphere of mass 3 kg and radius 0.2 m rolling down an inclined plane of height 7 m is : 42 J 60 J 36 J 70 J A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s . How much work is needed to stop it? 1 J 3 J 30 kJ 2 J Three identical spherical shells, each of mass M and radius R , are placed as shown in the figure. The moment of inertia of the system about an axis XX' passing through the center of one shell and tangent to the other two is: 12 3 MR 2 4MR 2 16 3 MR 2 3MR 2 The ratio of radii of gyration of a solid sphere and a hollow sphere of the same mass and radius about their diameters is: 3 : 5 2 : 3 2 : 3 3 : 5 A uniform square plate has side length a . The moment of inertia of this plate about an axis passing through its center and parallel to one of its sides is I . The moment of inertia of the same plate about a diagonal is: I 2I I 2 I 2 From a circular disc of radius R and mass 9M , a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its center is: 40/9 MR 2 4MR 2 37/9 MR 2 10/9 MR 2 Three identical rods each of mass M and length L are joined to form an equilateral triangle. The moment of inertia of the system about an axis passing through the center of mass and perpendicular to the plane of the triangle is: ML 2/2 ML 2/3 ML 2/4 ML 2/6 A wheel of radius 0.4 m can rotate freely about its axis. A string is wrapped over its rim and a mass of 4 kg is hung from it. An angular acceleration of 8 rad/s 2 is produced in it. The moment of inertia of the wheel is ( g = 10 m/s 2 ): 1.28 kg m 2 1.6 kg m 2 3.2 kg m 2 0.64 kg m 2 A circular disc of radius R and thickness R/6 has moment of inertia I about an axis passing through its center and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is: I/5 I/10 I/2 2I A thin wire of length L and uniform linear mass density is bent into a circular loop. The moment of inertia of this loop about the tangential axis in the plane of the loop is: 3ML 2 8 2 ML 2 8 2 5ML 2 8 2 ML 2 2 2 The ratio of the radii of gyration of a circular disc and a circular ring of the same mass and radius about a tangential axis in their plane is: 5 : 6 1 : 2 2 : 1 3 : 2 Three identical spherical shells each of mass m and radius r are placed such that their centers form an equilateral triangle of side 2r . The moment of inertia of the system about an axis passing through the center of one shell and perpendicular to the plane of the triangle is: 16 3 mr 2 4mr 2 20 3 mr 2 5mr 2 A thin uniform rod of length L and mass M is bent into a 'U' shape with three equal segments. The moment of inertia of this 'U' shape about an axis passing through the midpoints of the two parallel arms and perpendicular to the plane of the 'U' is: 1 12 ML 2 1 18 ML 2 1 9 ML 2 1 4 ML 2 A thin wire of length L and uniform linear mass density is bent into a square loop. The moment of inertia of this loop about an axis passing through the center of the square and perpendicular to its plane is: L 3 24 L 3 12 L 3 48 L 3 6 The moment of inertia of a uniform circular disc of mass M and radius R about an axis passing through its edge and perpendicular to its plane is: 3 2 MR 2 1 2 MR 2 5 4 MR 2 MR 2 The moment of inertia of a uniform equilateral triangular plate of mass M and side a about an axis passing through its vertex and perpendicular to the plate is: Ma 2 2 Ma 2 3 Ma 2 4 Ma 2 6 The moment of inertia of a thin uniform circular disc of mass M and radius R about an axis passing through the center and making an angle of 45 with the plane of the disc is: 3 8 MR 2 1 4 MR 2 1 2 MR 2 5 8 MR 2 Three identical rods each of mass m and length L are joined to form an 'H' shape. The moment of inertia of this system about an axis passing through the center of the middle rod and perpendicular to its plane is: 7 12 mL 2 1 2 mL 2 2 3 mL 2 5 6 mL 2 The moment of inertia of a thin uniform circular ring of mass M and radius R about an axis passing through its center and making an angle of 45 with the plane of the ring is: 3 4 MR 2 1 2 MR 2 1 4 MR 2 MR 2 A thin rod of length L has a linear mass density given by = kx where x is the distance from one end. The moment of inertia of the rod about an axis perpendicular to the rod and passing through the end x=0 is: 1 4 ML 2 1 3 ML 2 2 5 ML 2 1 2 ML 2 A point P lies on the axis of a ring of mass M and radius R at a distance R from its center. The moment of inertia of the ring about an axis passing through P and parallel to the plane of the ring is: 3 2 MR 2 MR 2 1 2 MR 2 2 MR 2 A solid sphere A of radius R and mass M is attached at a point to a smaller solid sphere B of radius r<R and mass m<M . Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of A is I A and that calculated about a vertical axis passing through the centre of B is I B . The difference I A-I B is: (M-m)(R+r) 2 (m-M)(R+r) 2 (m-M)(R-r) 2 0 A uniform disc of mass M and radius R is rotating about its central axis. If a small mass m is placed on its edge, the moment of inertia of the system becomes: ( M 2 + m)R 2 ( M+m 2 )R 2 ( M 2 )R 2 (M+m)R 2