Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_c$. Radius of gyration of the same disc about a diamter of the disc is $K_d$. the ratio $K_d : K_c$ is

A solid sphere of radius R and mass M is rotating about its diameter. The moment of intertia of the solid sphere rotating about an axis at a distance $\dfrac{R}{3}$ from the centre and parallel to that diameter is

A mass tied to a string is whirled in a horizontal circular path with a constant angular velocity and its angular momentum is 'L'. If the length of the string is now halved, keeping angular velocity same then the angular momentum will be

Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B = 225\, r_A$. If the orbital speed of the planet A is 'V' then the orbital speed of planet B will be