moment of inertia all questions

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1. Three balls of masses 2kg ,4kg and 6kg respectively are arranged at centre of the edges of an equilateral tringle of side 2m . The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of tringle will be ……………………kg𝒎^𝟐 (2024 ) 2.Ratio of radius of gyration of hollow sphere to that of a solid cylinder of equal mass , for moment of inertia about their diameter axis AB as shows in figure is √(𝟖/(𝒙 )) . The value of x is : (2024) 3.Two identical spheres each of mass 2kg and radius 50cm are fixed at the ends of a light rod so that the separation between the centre is 150cm , then moment of inertia of the system about an axis perpendicular to rod and passing through its middle point is 𝒙/𝟐𝟎 kg𝒎^𝟐 where the value of x is ……………2024 4.Four particles each of mass 1 kg are placed at four corners of a square of side 2m . Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is ………….. kg𝒎^𝟐 2024 5.A solid sphere and a solid cylinder of same and radius are rolling on a horizontal surfaces without slipping . The ratio of their radius of gyration respectively is 2: √𝒙 6.The moment of inertia of a semicircular ring about an axis passing through the centre and perpendicular to the plane of ring is 𝟏/𝒙 M𝑹^𝟐 ,the value of x is …………2023. 7.A ring and a solid sphere rotating about an axis passing through their cnters have same radii of gyration . The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is √(𝟐/𝒙) . The value of x is …………2023. 8. Moment of inertia of disc of mass M and radius R about any of its diameter is 〖𝑴𝑹〗^𝟐/𝟒 . The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be 〖𝒙 𝑴𝑹〗^𝟐/𝟐 . The value of x is ………..2023 9.Two discs of same mass and different radii are made of different materials such that their thickness are 1cm and 0.5cm respectively . The densities of material are in the ratio 3:5 . The moment of inertia of these discs respectively about their diameter will be in the ratio of 𝒙/𝟔 . The value of x is ……..2023 . 10.𝑰_𝑪𝑴 is moment of inertia of circular disc about an axis com passing through its center and perpendicular to the disc . 𝑰_𝑨𝑩 is its moment of inertia an axis AB perpendicular to plane and parallel to CM at a distance 𝟐/𝟑 R from centre . The ratio of 𝑰_𝑨𝑩 and 𝑰_𝑪𝑴is x: 9 . The value of x is ……………..2023. 11.If a solid sphere of mass 5kg and a disc of mass 4kg have the same radius . Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be 𝒙/𝟕 . The value of x ……………. 2023 . 12.Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5cm then its radius of gyration about PQ will be √𝒙 cm . The value of x is 13.Four identical discs of mass M and diameter ‘a’ are arranged in a small plane as shown in figure . If the moment of inertia of the system about OO’ is 𝒙/𝟒 M𝒂^𝟐 then the value of x is ………..2022 . 14.The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the centre will be ………..m . Given the length of the rod is 𝟏𝟎√𝟑 m . 2022 15.Four particles with a mass of 1kg , 2kg , 3kg and 4kg are situated at the corners of a square with side 1m . The moment of inertia of the system about an axis passing through the point O and perpendicular to the plane of the square is ……………….. 16.The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is 𝑰_𝟏 . The same rod is bent into a ring and its moment of inertia about a diameter is 𝑰_𝟐. 𝑰_𝟏/𝑰_𝟐 is 〖𝒙𝝅〗^𝟐/𝟑 then the value of x will be ………………. 2022 17.A system consists of two identical spheres each of mass 1.5kg and radius 50cm at the end of light rod . The distance between the centres of the two spheres is 5cm . What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint ? 18.75 kg𝒎^𝟐 1.905 x 〖𝟏𝟎〗^𝟓 kg𝒎^𝟐 19.05 kg𝒎^𝟐 1.875 x 〖𝟏𝟎〗^𝟓 kg𝒎^𝟐 18.Moment of inertia of a square plate of side L about the axis passing through one of the corner and perpendicular to the plane of square plate is given by : 〖𝑴𝑳〗^𝟐/𝟔 〖𝑴𝑳〗^𝟐 〖𝑴𝑳〗^𝟐/𝟏𝟐 〖𝟐𝑴𝑳〗^𝟐/𝟑 19.Mass per unit area of a circular disc of radius a depends on the distance r from its centre as 𝝈(𝒓) = A + Br . The moment of inertia of the disc about the axis perpendicular to the plane and passing through its centre is : 2𝝅𝒂^𝟒 ( 𝒂𝑨/𝟒+𝑩/𝟓) 2𝝅𝒂^𝟒 ( 𝑨/𝟒+𝒂𝑩/𝟓) 𝝅𝒂^𝟒 ( 𝑨/𝟒+𝒂𝑩/𝟓) 2𝝅𝒂^𝟒 ( 𝑨/𝟒+𝑩/𝟓)