A solid sphere of radius `3R`, a solid disc of radius `2R` and a ring of radius `R` (all are of mass `m`) roll down a rough inclined plane. Their accelerations are `a,b` and `c` respectively. Find the ratio of `a//b` and `b//c`.

Answer

`0015`

Explanation

Since `S = (1)/(2) at^(2)` so, `S_(1) = (1)/(2) a_(1) t^(2)`…(1)
& `S_(2) = (1)/(2) a_(2) t^(2)`…(2)
from (1) & (2) `S_(1) -S_(2) = (1)/(2)(a_(1) - a_(2)) t^(2)` …(3)
for pure rolling on inclined plane
`a = (g sin theta)/(1 + K^(2) //R^(2))` so, for solid cylinder
`a_(1) = (g sin 30^@)/(1 +1//2) =(g)/(3)`
for hollow cylinder `a_(2) =(g sin 30^@)/(1+1) =(g)/(4)`
Putting the value of `a_(1)` & `a_(2)` in equation (3)
`S_(1) -S_(2) =(1)/(2) ((g)/(3) -(g)/(4))6^(2) rArr S_(1) -S_(2) = (3g)/(2)`
`S_(1) -S_(2) = 15 m//s`.