A round uniform body of radius ‘R’ , mass ‘M’ and moment of inertia ‘I’, rolls down (without slipping)and inclined plane…

Q: A round uniform body of radius ‘R’ , mass ‘M’ and moment of inertia ‘I’, rolls down (without slipping)and inclined plane making an angle ‘θ’ with the horizontal. Then, its acceleration is

Sol: $\large v = \sqrt{\frac{2 g h}{1+\frac{I}{MR^2}}}$

$\large h = L sin\theta $

$\large v^2 = u^2 – 2 a s$

$\large a = \frac{v^2}{2 s} = \frac{2 g L sin\theta}{2(1+\frac{I}{MR^2})L}$

$\large a = \frac{g sin\theta}{(1+\frac{I}{MR^2})}$