A circular disc reaches from top to bottom of an inclined plane of length l . When it slips down the plane, if takes t ~s . When it rolls down the plane then it takes ( 2 )^ 1 / 2 t ~s , where is _________

Step-by-step solution

For slipping aligned & a = g & = 1 2 at ^2 t = 2 g aligned For rolling aligned & a ^ = g 1+ k ^2 R ^2 [ k = R 2 ] & a ^ = 2 ~g 3 & = 1 2 a ^ ( t ^ )^2 & t ^ = 6 2 ~g = 2 2 g & =3 aligned