A thin ring and solid cylinder are placed on the top of a rough incline and they are allowed to roll down the incline without slipping. If the ring arrives at the bottom of incline in 5 s, The cylinder will arrive at the bottom in time

ar = Acceleration of ring = gsinθ1+Imr2=gsinθ1+mr2mr2=12gsinθac= Acceleration of the cylinder = gsinθ1+12mr2mr2=23gsinθIf length of inclined plane is s, The time taken by the ring , tr=2sar and the time taken by the cylinder, tc=2sac∴tctr=arac=34=32⇒tc=5 x 32s=532s.