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 havethe largest speed
C. sphere (iii) will have the largest kinetic energy
D. all the sphere will have equal speeds.

Answer

D

Explanation

Acceleration, `a=(g sin theta)/(1+(I)/(mv^(2)))`
For a sphere, `(I)/(mv^(2))=(2)/(5)`
Hence, `a=(5)/(7)g sin theta=` constant,
Hence, speed of all sphere is same at the bottom. Sphere (ii) has the largest mass. Hence, it will have the maximum kinetic energy.