A) Solid sphere
B) Hollow sphere
C) Disc
D) All will reach in same time
Correct Answer: A
Solution :
The acceleration of a body rolling down an inclined plane is \[a=\frac{g\sin \theta }{(1+I/M{{r}^{2}})}\] For solid sphere, \[I=\frac{2}{5}M{{R}^{2}}\] \[\therefore \] \[a=\frac{5}{7}g\sin \theta \] For hollow sphere, \[I=\frac{2}{3}M{{R}^{2}}\] \[\therefore \] \[a=\frac{3}{5}g\sin \theta \] For disc,\[I=\frac{1}{2}M{{R}^{2}}\] \[\therefore \] \[a=\frac{2}{3}g\sin \theta \] Acceleration is maximum for solid sphere hence, the solid sphere will reach the bottom in the least time.
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