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
- $\frac{g\,sin\,\theta}{1+\frac{I}{MR^{2}}}$
- $\frac{g\,sin\,\theta}{1+\frac{MR^{2}}{I}}$
- $\frac{g\,sin\,\theta}{1-\frac{I}{MR^{2}}}$
- $\frac{g\,sin\,\theta}{1-\frac{MR^{2}}{I}}$
The Correct Option is A
Solution and Explanation
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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.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.