A solid rolls down two different inclined planes of the same heights but different angle of inclination. Will it take longer to roll down one plane than the other ?

A solid rolls down two different inclined planes of the same heights b

1.	A solid rolls down two different inclined planes of the same heights but different angle of inclination. Will it take longer to roll down one plane than the other ?
Answer» Solution :We know that `a=(gsintheta)/(1+(K^2)/(R^2))` where `R^2=2/5R^2` `:. A=5/7gsintheta"":.apropsintheta` We also note that `s_1=1/2a_1t_1^2` and `s_2=1/2a_2t_2^2` i.e `s_1=1/2xx5/7gsintheta_1t_1^2=((5G)/(12))sintheta_1t_1^2` i.e `t_1^2=((12s)/(5gsintheta_1))` similarly, `t_2^2=(12s)/(5gsintheta_2)` Here `s_2>s_1` and `theta_2t_1` i.e. Time TAKEN for the sphere in the second case with smaller inclination is more than that for the PLANE with greater inclination