The ratio of the time taken by a solid sphere and that taken by a disc of the same mass and radius to roll down a rough inclined plane from rest, from the same height is

The ratio of the time taken by a solid sphere and that taken by a disc

1.	The ratio of the time taken by a solid sphere and that taken by a disc of the same mass and radius to roll down a rough inclined plane from rest, from the same height is
Answer» `15:14` `sqrt(15) : sqrt(14)` `14 : 15` `sqrt(14) : sqrt(15)` Solution :In CASE of pure rolling, `a=(g SIN THETA)/(1+(I)/(mR^(2)))` `(I)/(mR^(2))=(2)/(5)` for sphere and `(I)/(MR^(2))=(1)/(2)` for a disc `:.` For a solid sphere, `a_(1)=(5)/(7)g sin theta` and for a hollow sphere, `a_(2)=(2)/(3)g sin theta` From `s=(1)/(2)at^(2),t=sqrt((2s)/(a))or (t_(1))/(t_(2))=sqrt((a_(2))/(a_(1)))=sqrt((2//3)/(5//7))=sqrt((14)/(15))`.