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Question #42376

Difficulty: 8/10 | 🟢 Free

The Question

A uniform solid disk of original mass $9m$ and radius $R$ has a circular hole of radius $R/3$ cut out. The hole is centered at a distance $2R/3$ from the geometric center $O$ of the disk. The remaining non-uniform disk (mass $8m$ ) is suspended by a light inextensible string wrapped around its outer rim. The string passes over an ideal fixed pulley at the edge of a smooth horizontal table and is attached to a block of mass $4m$ resting on the table. At $t=0$ , the system is released from rest with the hole's center located exactly to the right of $O$ at the same horizontal level. The string unwinds vertically from the left edge of the disk. Find the initial acceleration of the block.

Options

A.
$\frac{71}{167} g$
B.
$\frac{2}{5} g$
C.
$\frac{71}{134} g$
D.
$\frac{66}{167} g$

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

Moment of Inertia (MOI) Symmetry|Constraint Relations via String Length|Frame of Reference Dependency

Why This Question Is Tricky

Common Mistakes

This question tests the frame of reference dependency in rigid body constraints and the application of the parallel axis theorem for non-symmetric mass distributions.

A common 'lethal collision' occurs when students blindly apply the constraint $a = \alpha R$ or assume the center of mass remains at the geometric center $O$ .

Because the axle is accelerating, the correct tangential constraint at the rim is $a_{string} = a_O - \alpha R$ .

Furthermore, the cutout shifts the center of mass, requiring the torque equation to be written strictly about the new CM (or about $O$ with the inclusion of a pseudo-force torque $-M \vec{r}_{cm} \times \vec{a}_O$ ).

Ignoring the CM shift leads directly to the trap answer of $2g/5$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Moment of Inertia (MOI) Symmetry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free