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)-
(A)(see structure)
(B)(see structure)✓ Correct
(C)(see structure)
(D)(see structure)
Answer: (B)
Solution
For rolling without slipping at the ground: V_center = ωR, where R = 10 cm is the radius of the roller. The velocity of the scale = V_center + ωr, where r = 5 cm is the radius of the axle. Given that V_center · t = 50 cm, the distance moved by the scale = (V_center + ωr)t = (V_center + V_center·r/R)t = (V_center)(1 + r/R)t = (3V_center/2)t = (3/2) × 50 = 75 cm. Therefore, the relative displacement of the scale with respect to the center of the roller is 75 - 50 = 25 cm to the right.
JEE Advanced · 2020 · 27 Sep 2020 · Paper 1 · Single correct option
