A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first?

Acceleration of a body rolling down an inclined plane is given by the following expression

a = g sinθ / 1 + k² / r²

θ is angle of inclination, k is radius of gyration and r is radius of the body rolling down.

for solid sphere

k² / r² = 2 / 5

=.4

a = g sinθ / 1.4

= 7 sinθ

for spherical shell

k² / r² = 2 / 3

=.67

a = g sinθ / 1.67

= 5.87 sinθ

for solid cylinder

k² / r² = 1/2

=.5

a = g sinθ / 1.5

= 6.53 sinθ

for cylindrical shell

k² / r² = 1

a = g sinθ / 2

= 4.9 sinθ

Acceleration of solid cylinder is maximum (7 sinθ)

so it will reach bottom first.