The following bodies, (1) a ring, (2) a disc, (3) a solid cylinder and (4) a solid sphere, of the same mass m and radius R are allowed to roll down without slipping simultaneously from the top of an inclined plane. The body which will reach first at the bottom of the inclined plane is ______. (Mark the body as per its respective numbering given in the question.)

All four start from rest and cover the same distance, so the one with the largest acceleration arrives first.

a=(g sin θ)/(1+k) with k=I/(mR²), so the largest acceleration goes with the smallest k.

Ring: k=1. Disc: k=1/2. Solid cylinder: k=1/2. Solid sphere: k=2/5.

The smallest is 2/5, the solid sphere.

The answer is 4.

Note that (2) and (3) are the same body as far as this calculation goes — a disc and a solid cylinder both have k=1/2 — so they would arrive together, in second place.

Mass and radius are the same for all four, but they would have cancelled anyway: only shape decides the order.