Consider three solid spheres, sphere (i) has radius r and mass m, sphere (ii) has radius r and mass 3 m, sphere (iii) has radius 3r and mass m, All can be placed at the same point on the same inclined plane, where they will roll without slipping to the bottom, If allowed to roll down the incline, then at the bottom of the incline

Options

A. sphere (i) will have the largest speed
B. sphere (ii) will have the largest speed
C. sphere (ii) will have the largest kinetic energy
D. all the spheres will have equal speed

Answer

C, D

Explanation

`mgh=1/2mv^(2)[1+(k^(2))/(R^(2))], k=` radius of gyration.For all solid spheres, `k/R=2v^(2)//5=` independent of `m` and `R`.