A solid sphere of mass m and radius r is released from rest at the top of smooth inclined plane of inclinationtheta. The ratio of acceleration when it rolls down the plane without slipping and when it slipping down the plane is

A solid sphere of mass m and radius r is released from rest at the top

1.	A solid sphere of mass m and radius r is released from rest at the top of smooth inclined plane of inclinationtheta. The ratio of acceleration when it rolls down the plane without slipping and when it slipping down the plane is
Answer» `7/5` `5/7` `3/7` `8/7` Solution :When the SPEHRE rolls down the plane without SLIPPING, the acceleration down the plane is `a_(1)=(g sin theta)/(1+K^(2)//R^(2))=(g sin theta)/(1+(2//5r^(2))/(r^(2))` `=(g sin theta)/(((5+2)/4))` `=5/7 g sin theta [:' K^(2)=2/5r^(2)]` When the sphere SLIDES down the plane, the acceleration is `a_(2)=g sin theta` `:. (a_(1))/(a_(2)0=5/7 XX(g sin theta)/(g sin theta)=5/7`