A) Solid cylinder
B) Hollow cylinder
C) Both will reach at the same time
D) Cannot be predicted
Correct Answer: A
Solution :
The acceleration of a body down an incline is given by \[a=\frac{g\sin \theta }{1+\frac{{{K}^{2}}}{{{R}^{2}}}}\] where K is radius of gyration, R the radius of the body. For a hollow cylinder moment of inertia\[I\]is \[I=M{{R}^{2}}\] For a solid cylinder \[I=M{{\left( \frac{R}{\sqrt{2}} \right)}^{2}}\] Also, \[I=M{{K}^{2}}\] \[\therefore \] \[{{K}_{solid}}<{{K}_{hollow}}\] \[\Rightarrow \] \[acceleratio{{n}_{Solid}}>acceleratio{{n}_{hollow}}\] Hence, solid cylinder will reach first.
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