Question

A rigid rod OA rotates clockwise at an angular velocity of 10 rad/s. A bead B (OB = 1 m) translates outward on the rod at a speed of 5 m/s and acceleration 2.5 m/s² (both quantities with respect to the rod). The Coriolis component of acceleration is
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• A. 2.5 m/s² in +x direction
• B. 100 m/s² in +x direction
• C. 100 m/s² in -y direction
• D. 25 m/s² in +y direction

Hint:

The Coriolis acceleration is given by \( a_c = 2v\omega \), and it acts perpendicular to the velocity direction of the object.

Answer 1

The Correct Option is B

The Coriolis acceleration is given by: \[ a_c = 2v\omega \] where \( v \) is the linear velocity of the bead, and \( \omega \) is the angular velocity. The bead is moving with a velocity of \( v = 5 \, \text{m/s} \) and the angular velocity of the rod is \( \omega = 10 \, \text{rad/s} \). Substituting these values into the formula, we get: \[ a_c = 2 \times 5 \times 10 = 100 \, \text{m/s}^2 \] The Coriolis acceleration acts in the direction perpendicular to the velocity vector, which is along the \( +x \) direction (as the motion is outward on the rod). Therefore, the Coriolis acceleration is \( 100 \, \text{m/s}^2 \) in the \( +x \) direction.
Step 2: Conclusion.
The correct answer is (B) 100 m/s² in the +x direction.
Final Answer: (B) 100 m/s² in +x direction