A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radius R is placed horizontally at rest with its length parallel to the edge such that the axis of the cylinder and the horizontal edge are in same vertical plane shown in the figure. There is sufficient friction present at the edge, so that a very small displacement causes the cylinder to roll off the edge without slipping. Then the ratio of the translational to rotational kinetic energies of the cylinder when its center of mass is in horizontal line with the edge is ...
Physics · Mixed Chapter
JEE Mains

Question

A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radius R is placed horizontally at rest with its length parallel to the edge such that the axis of the cylinder and the horizontal edge are in same vertical plane shown in the figure. There is sufficient friction present at the edge, so that a very small displacement causes the cylinder to roll off the edge without slipping. Then the ratio of the translational to rotational kinetic energies of the cylinder when its center of mass is in horizontal line with the edge is ...

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Under pure rolling about a stationary edge with no slip, the instantaneous contact point has zero velocity; the centre moves with speed v꜀ₘ=ωR for a cylinder of radius R. Step 2: Translational kinetic energy is Kₜᵣₐₙₛ=(1/2)Mv꜀ₘ²=(1/2)MR²ω². For a homogeneous solid cylinder, I꜀ₘ=(1/2)MR², so rotational kinetic energy is Kᵣₒₜ=(1/2)I꜀ₘω²=(1/4)MR²ω². Step 3: The direct calculation for the usual translational/rotational split gives Kₜᵣₐₙₛ/Kᵣₒₜ=2, whereas the source key prints 6. Verification…