The variation of acceleration due to gravity $$g$$ with distance d from centre of the earth is best represented by (R = Earth’s radius):

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :

A slender uniform rod of mass M and length $$l$$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $$\theta$$ with the vertical is

The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$. What is the ratio $${l \over R}$$ such that the moment of inertia is minimum?