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  4. 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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Q. 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)Physics Question Image

JEE AdvancedJEE Advanced 2020

Solution:

image
$v -\omega R =0$
$v_{p}=v+\omega r=v+\frac{v}{R} r=v\left(1+\frac{r}{R}\right)$
So, $\Delta x _{ p }=50\left(1+\frac{5}{10}\right)=75 \,cm$