The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle theta without slipping and slipping down the incline without rolling is

The ratio of the accelerations for a solid sphere (mass m and radius R

1.	The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle theta without slipping and slipping down the incline without rolling is
Answer» `5 : 7` `2 : 3` `2 : 5` `7 : 5` Solution :ACCELERATION of the SOLID SPHERE SLIPPING down the incline without rolling is `a_("slipping") = g sin theta "" …. (i)` Acceleration of the solid sphere rollind down the incline without slipping is `a_("rolling")= (g sin theta)/(1 + (k^(2))/(R^(2))) = (a sin theta)/(1 + 2/5) ( because` For solid sphere , `(k^2)/(R^2) = (2)/(5)`) `= (5)/(7) g sin theta "" ... (ii)` Divide eqn. (ii) by eqn.(i) , we get `(a_("rolling"))/(a_("slipping")) = (5)/(7)`