Given, Three bodies be ring, solid cylinder and solid sphere, initial speed (u) be zero. Etotal =(KE)rot+(KE)trans =mgh h be the height of inclined plane. ∴
1
2
Iω2+
1
2
mv2=mgh ⇒
1
2
I
v2
R2
+
1
2
mv2=mgh ⇒v2=√
2mgh
I
R2
+m
where, v= velocity of body at bottom (v=Rω) I= moment of inertia, ω= angular frequency, m= mass of body and R= radius of body. ∵Iring =MR2 Isolid cylinder =
MR2
2
=0.5MR2 Isolid sphere =
2
5
MR2=0.4MR2 ∴ From equation v∝
1
√I
and Iring >Isolid cylinder >Isolid sphere ∴vring is least.