Q 1 :    

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for the moment of inertia about their diameter axis AB as shown in the figure, is $\sqrt{8/x}$. The value of $x$ is        [2024].

• 17

   

• 34

   

• 67

   

• 51

   

Q 2 :    

Three balls of masses 2 kg, 4 kg, and 6 kg respectively are arranged at the center of the edges of an equilateral triangle of side 2 m. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of the triangle will be ____ kg ${\mathrm{m}}^2$.    [2024]

Q 3 :    

Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ ${\mathrm{kgm}}^2$.     [2024]

Q 4 :    

Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is $x/20$ ${\mathrm{kgm}}^2$, where the value of $x$ is _____.          [2024]