11.Two wheels, each with four spokes, are mounted one behind the other and aligned such that an observer sees only four spokes. At t =0 minute, one wheel begins to spin at 5 revolutions/ minute and the other at 4 revolutions / minute. Upto t = 1 minute, how many times the observer would see only four spokes ?

12.A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is

13.A particle is projected so as to just move along a vertical circle. The ratio of the tensions in the string when the particle is at the lowest and highest point on the circle is

14.A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. The angular speed will approximately

15.When a sphere rolls without slipping the ratio of kinetic energy of translation to its total kinetic energy is