Question

a circular ring and a disc of same mass ' m' and radius' r' roll down an inclined plane. which one will reach the bottom first? which one will gain higher velocity?

Answer 1

As the ring's moment of inertia is higher (double) than that of the disc, it will gain less velocity.  So the disc travels faster and reaches the bottom first.

disk radius = r             mass = m
Moment of inertia = I1 = 1/2 m r²
ring radius = r         mass = m
moment of inertia = I2 = m r² = 2 * I1

When they roll down the inclined plane,
      the KE = 1/2 m v² + 1/2 I ω²= m g h 
         Ring:    v² = g h
         Disc:     v²  = 4/3 * g h