In figure E and v_ cm represent the total energy and speed of centre of mass of an object of mass 1 ~kg in pure rolling. The object is

Step-by-step solution

As we know, kinetic energy of an object in pure rolling motion is given as E= 1 2 m v_ cm ² (1+ k² R² ) where, k is radius of gyration and m is the mass of the object. E v_ cm ² = 1 2 [1+ k² R² ] ...(i)[ Given, m=1 ~kg ] From the given graph, substituting the value of E v_ cm ² in Eq. (i), we get aligned 3 4 &= 1 2 [1+ k² R² ] 3 2 -1 &= k² R² k² R² &= 1 2 aligned Since, for a (a) Sphere, k² R² = 2 5 (b) Ring, k² R² =1 (c) Hollow cylinder, k² R² =1 (d) Disc, k² R² = 1 2 So, the given object is disc.