A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is

A ring and a disc roll on the horizontal surface without slipping with

1.	A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is
Answer» 3 J 4 J 5 J 6 J Solution :Total kinetic energy of the ring it rolls without SLIPPING , `K_("ring") = K_(T) + K_(R) = (1)/(2) mv^(2) + (1)/(2) I , omega^(2)` = `(1)/(2) mv^(2) + (1)/(2) MR^(2) XX (v^(2))/(r^(2)) = mv^(2) "" (because I_(Y) = mr^(2) and omega = (v)/(r))` But `K_("ring") =4 J` (given) `thereforemv^(2) = 4 J "" ... (i)` Similarly , `K_("disc") = (1)/(2) mv^(2)+ (1)/(2) I_(d) omega^(2)` `= (1)/(2) mv^(2) + (1)/(2) xx (mr^(2))/(2) xx (v^(2))/(r^(2)) ( because I_(d) = (mr^(2))/(2))` `= (3)/(4) mv^(2) = (3)/(4) xx 4 J = 3J "" ` (Using (i))