Answer:
A ) SOLID SPHERE
Explanation:
Moment of inertia of solid sphere = 2/5 M R²
= M K² , K is called radius of gyration
K = √2/5 R
Moment of inertia of solid cylinder = 1/2 M R²
= M K² , K is called radius of gyration
K = 1 /√2 R
Moment of inertia of solid sphere = M R²
= M K² , K is called radius of gyration
K = R
For rolling on inclined plane , acceleration
a =
Putting the value of K for solid sphere
a for solid sphere
a = g sinθ / ( 1 +2/5)
a = .714 g sinθ
Putting the value of K for solid cylinder
a for solid cylinder
a = g sinθ / ( 1 +1/2)
a = .666 g sinθ
Putting the value of K for hollow pipe
a for hollow pipe
a = g sinθ / ( 1 +1 )
a = . 5 g sinθ
So we see that acceleration a for solid sphere is greatest and a for hollow pipe is the least. Hence solid sphere will reach the bottom earliest and hollow pipe will reach the bottom the latest.