Question:
A round uniform body of radius $R$, mass $M$ and moment of inertia $I$, rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration
A round uniform body of radius $R$, mass $M$ and moment of inertia $I$, rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration
Updated On: Jul 14, 2022
- $\frac{g\,sin\,\theta}{1+\frac{I}{MR^{2}}}$
- $\frac{g\,sin\,\theta}{1+\frac{MR^{2}}{I}}$
- $\frac{g\,sin\,\theta}{1-\frac{I}{MR^{2}}}$
- $\frac{g\,sin\,\theta}{1-\frac{MR^{2}}{I}}$
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The Correct Option is A
Solution and Explanation
$Mg\,sin\,\theta-f=Ma$
$fR=I \frac{a}{R}$
$\Rightarrow a=\frac{g\,sin\,\theta}{\left(1+\frac{I}{MR^{2}}\right)}$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
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