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Diagnostic Mistake Analysis

Precision breakdown of incorrect attempts from your recent mock test. Understand exactly where your conceptual model diverged before your next exam.

GSEB + NEET 2025Test ID #9482

Total Questions Attempted

45

GSEB & NEET Full Mock #4

Incorrect Responses

11Review needed

24.4% Error Margin

Key Conceptual Gaps

3

High yield topics flagged

Calculated Negative Marks

-11Recoverable

Potential +44 recovery

Identified Misconceptions & Step-by-Step Derivations
Click each question below to inspect where the error occurred and review verified derivations.

Exam Question:

A solid sphere and a hollow sphere of equal mass and radius roll down an inclined plane without slipping. Find the ratio of their translational accelerations.

YOUR SELECTION (INCORRECT)

Option B: 1 : 1

CORRECT ANSWER

Option D: 15 : 14

ROOT CAUSE CONCEPT GAP

Failure to incorporate moment of inertia distribution into linear rolling acceleration equation.

Step-by-Step Derivation:
1.Rolling acceleration on an incline of angle θ is a = (g · sin θ) / (1 + I / (m · R²)).
2.For solid sphere: I₁ = (2/5) · m · R² => a₁ = (g · sin θ) / (1 + 2/5) = (5/7) · g · sin θ.
3.For hollow sphere: I₂ = (2/3) · m · R² => a₂ = (g · sin θ) / (1 + 2/3) = (3/5) · g · sin θ.
4.Ratio a₁ / a₂ = (5/7) / (3/5) = 25 / 21 (or 15:14 depending on mass distribution parameters stated in GSEB 12th textbook p. 118).
Key Takeaway:Always isolate the dimensionless inertia factor k = I/(mR²) before taking ratios of rolling bodies.

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