A disk of radius R rolls without slipping simultaneously between two plates moving at the velocities indicated in the figure. If disk angular speed is NV/(3R), find N.
Physics · Mixed Chapter
JEE Main Practice

Question

A disk of radius R rolls without slipping simultaneously between two plates moving at the velocities indicated in the figure. If disk angular speed is NV/(3R), find N.

G1 Physics · Accepted Answer

Step 1: No slip means velocity of top disk contact equals upper plate velocity v_top, and bottom contact equals lower plate velocity v_bottom. Step 2: For disk centre speed v_C and angular speed ω: v_top=v_C−ωR and v_bottom=v_C+ωR (with sign convention chosen). Step 3: Subtract: |ω|=|v_bottom−v_top|/(2R). Step 4: Source gives N=3 and therefore |ω|=V/R. The figure's exact lower-plate speed label is not legible; independently check the signed plate speeds before publication.