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GATE 2025 ME – Question 26

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 1 mark · Multiple choice

A rigid circular disc of radius $r$ (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega$ (in rad s$^{-1}$). The velocities (in m s$^{-1}$) at points $O$ and $A$, respectively, are

A disc with centre O and its lowest point A touching the ground, rotating anticlockwise with angular velocity $\omega$. The unit vectors $\hat{i}$ (to the right) and $\hat{j}$ (up) are shown.
  1. $r\omega\,\hat{i}$ and $0\,\hat{i}$
  2. $-r\omega\,\hat{i}$ and $0\,\hat{i}$
  3. $-r\omega\,\hat{i}$ and $-r\omega\,\hat{i}$
  4. $r\omega\,\hat{i}$ and $r\omega\,\hat{i}$

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Show answer and explanation

Correct answer: (A) $r\omega\,\hat{i}$ and $0\,\hat{i}$

Explanation

The point A touches the ground and does not slip, so its velocity is zero. The centre O is at a distance $r$ from A and has speed $r\omega$. An anticlockwise rotation makes the disc roll to the right, so $v_O = r\omega\,\hat{i}$.