AP EAMCET · PHYSICS · Rotational Motion
A solid sphere of mass 4 kg and radius 28 cm is on an inclined plane. If the acceleration of the sphere when it rolls down without sliding is \(3.5 \mathrm{~m} \mathrm{~s}^{-2}\), then the acceleration of the sphere when it slides down without rolling is
- A \(2.5 \mathrm{~m} \mathrm{~s}^{-2}\)
- B \(3.5 \mathrm{~m} \mathrm{~s}^{-2}\)
- C \(1.7 \mathrm{~m} \mathrm{~s}^{-2}\)
- D \(4.9 \mathrm{~m} \mathrm{~s}^{-2}\)
Answer & Solution
Correct Answer
(D) \(4.9 \mathrm{~m} \mathrm{~s}^{-2}\)
Step-by-step Solution
Detailed explanation
\(a_{\text{roll}} = \frac{g \sin\theta}{1 + \frac{I}{mR^2}}\) \(a_{\text{roll}} = \frac{g \sin\theta}{1 + \frac{2/5 mR^2}{mR^2}} = \frac{g \sin\theta}{7/5} = \frac{5}{7}g \sin\theta\) \(3.5 = \frac{5}{7}g \sin\theta\)…
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