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Question #42096

Difficulty: 8/10 | 🟢 Free

The Question

A small block of mass $m$ is placed on a rough horizontal turntable rotating with a constant angular velocity $\omega$ about a vertical axis. At $t=0$ , the block is at a distance $R$ from the axis and is given an initial velocity $v_0$ directed radially outward relative to the turntable. If the coefficient of kinetic friction between the block and the turntable is $\mu_k$ , what is the radius of curvature of the block's trajectory in the reference frame of the turntable at $t=0$ ?

Options

A.
$\frac{v_0}{2\omega}$
B.
$\frac{v_0^2 \sqrt{v_0^2 + \omega^2 R^2}}{2\omega v_0 \sqrt{v_0^2 + \omega^2 R^2} + \mu_k g \omega R}$
C.
$\frac{v_0^2}{2\omega v_0 + \mu_k g}$
D.
$\frac{v_0^2}{|\omega^2 R - \mu_k g|}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Centripetal Acceleration Vector|Angular Velocity vs Linear Velocity|Kinetic Friction Transition

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of non-inertial reference frames and the fundamental nature of kinetic friction.

A lethal trap for students is assuming that kinetic friction opposes the velocity of the block relative to the ground ( $\vec{v}_g = v_0 \hat{i} + \omega R \hat{j}$ ).

This misconception incorrectly introduces a tangential component of friction, leading to Option B.

Furthermore, it evaluates whether students correctly identify that the initial radius of curvature in the rotating frame depends exclusively on the Coriolis acceleration, as the radial acceleration (centrifugal and friction) is parallel to the initial relative velocity vector and thus does not contribute to the cross product.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Centripetal Acceleration Vector
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free