A small roller of diameter $$20$$ cm has an axle of diameter $$10$$ cm (see$$ figure below on the $$left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see$$ figure on the $$right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved $$50$$ cm, the position of the scale will look like $$(figures$$ are schematic and not drawn to $$scale)-$$

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Infinity Learn · Accepted Answer

For no slipping at the ground,Vcentre $$=$$ωR  (R$$ is radius of $$roller) ∴ Velocity of scale $$=Vcenter$$ $$+$$ωr [r is radius of axle]  Given, Distance moved by roller $$=Vcenter$$ ×$$t=50cm$$∴ Distance moved by scale $$=Vcenter$$ $$+$$ω$$rt=Vcenter$$ $$+Vcenter$$ $$rRt=3Vcenter$$ $$2$$⋅$$t=3$$×$$502=75cm$$

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