Question

Three objects roll without slipping from rest down an inclined plane. A solid sphere with I₁= 2/5 MR², a hollow solid cylinder I = MR², and a solid cylinder with I₂ = 1/2 MR². Which of the objects will reach the bottom of the inclined plane first? Use conservation of energy for translation and rotational motion.

Answer 1

For so lid sphere I= 2 M R² = Mk? S R? W Nin R. 5 For Hl. So bied cylinder I .=MR²-MI? -) 6² = h MR² = MK For Solid Cylinder I - + 2 - K? - R2 where ka radius of gyration Acc. to conservation of energy occeleration is given by ug hina i ax I I+K? R2 is least (int) Since K² for sphere, :.it will have maximum acceleration and hence will reach the bottom first