The total kinetic energy of a body of mass 10 kg and radius 0.5 m moving with velocity of 2 m/s without slipping is 32.8 J. The radius of gyration of a body is ………..

The total kinetic energy of a body of mass 10 kg and radius 0.5 m movi

1.	The total kinetic energy of a body of mass 10 kg and radius 0.5 m moving with velocity of 2 m/s without slipping is 32.8 J. The radius of gyration of a body is ………..
Answer» `0.25m` `0.2m` `0.5m` `0.4m` SOLUTION :TOTAL energy of rolling BODY `E=(1)/(2)mv^(2)(1+(k^(2))/(R^(2)))" "["where "V_(CM)=v]` `THEREFORE 32.8xx2=10xx(2)^(2) [1+(k^(2))/((0.5)^(2))]` `therefore (65.6)/(10xx4)=1+(k^(2))/(0.25^(2))` `therefore 1.64=1+(k^(2))/(0.25)` `therefore 0.64=(k^(2))/(0.25)` `therefore k^(2)=0.64xx0.25` `therefore k=0.8xx0.5` `therefore k=0.4m`