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Question #42396

Difficulty: 8/10 | 🟢 Free

The Question

A uniform solid cylinder of radius $r$ and height $h=4r$ rests upright on a rough horizontal turntable. The center of its base is at a distance $R = 4 \text{ m}$ from the rotation axis. The turntable starts from rest at $t=0$ . The arc length $s(t)$ traveled by the cylinder's base is recorded, and its $s-t$ graph is a parabola with a constant concavity $\frac{d^2s}{dt^2} = 3 \text{ m/s}^2$ . The coefficient of static friction is $\mu = 0.8$ . Taking $g = 10 \text{ m/s}^2$ , determine the mode of instability (sliding or toppling) and the exact time $t$ it occurs.

Options

A.
$\text{Topples at } t = \frac{4}{3} \text{ s}$
B.
$\text{Slides at } t = \frac{4}{3} \text{ s}$
C.
$\text{Topples at } t = \frac{2\sqrt{5}}{3} \text{ s}$
D.
$\text{Slides at } t = \frac{2\sqrt{5}}{3} \text{ s}$

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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

Toppling vs Sliding|Graphical Concavity Significance|Angular Velocity vs Linear Velocity

Why This Question Is Tricky

Common Mistakes

This question tests the transition from static equilibrium to dynamic instability in non-uniform circular motion.

A common trap is ignoring the tangential Euler force ( $ma_t$ ) and only considering the radial centrifugal force ( $ma_r$ ) when calculating the toppling torque, which leads to the incorrect time $t = \frac{2\sqrt{5}}{3} \text{ s}$ .

Furthermore, students must evaluate both the friction-limited sliding condition ( $\mu mg$ ) and the torque-limited toppling condition to correctly identify the mode of failure.

The graphical concavity constraint ensures students derive the instantaneous acceleration rather than assuming uniform circular motion.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Toppling vs Sliding
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free