JEE Advanced 2020 · Paper 1 · Physics Q3

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PhysicsSingle correct+3 / -1Question 3 of 54

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)

Perspective drawing of the roller: a wide cylinder (diameter 20 cm) with a narrower hatched axle (diameter 10 cm) protruding from both faces.

Side view: the roller (shaded outer circle) with its hatched axle; a horizontal meter scale rests on top of the axle with its right edge at the top of the axle, extending to the left.

Side view of the roller (outer circle, diameter 20 cm, with the hatched axle, diameter 10 cm) with the scale lying on top of the axle. Dashed lines mark the scale's x = 0 end (its left end) and the scale reading x = 50 cm, which sits directly above the roller's axis; the scale extends past the roller to the right.

Side view of the roller with the scale lying on top of the axle. The scale's x = 0 end is directly above the roller's axis and the scale extends to the right, its x = 100 cm end marked by a dashed line.

Answer and worked solution

Official answer: B

Velocities. The roller (radius 10 cm) rolls without slipping, so $v_c=\omega\cdot10$ . The top of the axle (radius 5 cm) moves at
$v_c+\omega\cdot5=1.5\,v_c.$

Displacements. The scale does not slip on the axle, so it moves $1.5\times50=75$ cm while the roller's axis moves 50 cm. Relative to the axle the scale therefore advances 25 cm.

Where the scale now touches. At the start the axle was under the scale's 100 cm edge. It is now under the mark $100-25=75$ cm, i.e. $x=0$ is 75 cm behind the axle and only 25 cm of scale is beyond it.

(B)

Topics:Rolling motion Relative velocity

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JEE Advanced 2020 · Paper 1, Physics question 3