If a solid sphere of mass 1 kg and radius 0.1 m rolls without slipping at a uniform velocity of 1 m/s along a straight line on a horizontal floor, the kinetic energy is ……….

If a solid sphere of mass 1 kg and radius 0.1 m rolls without slipping

1.	If a solid sphere of mass 1 kg and radius 0.1 m rolls without slipping at a uniform velocity of 1 m/s along a straight line on a horizontal floor, the kinetic energy is ……….
Answer» `(7)/(5)J` `(2)/(5)J` `(7)/(10)J` `1J` SOLUTION :Total kinetic energy of ball rolling on a horizontal SURFACE = (translational kinetic energy) + (rotational kinetic energy) `=(1)/(2)mv^(2)+(1)/(2)I.omega^(2)` Moment of inertia `I=(2)/(5)MR^(2)` (for sphere) and `omega=(v)/(R )` `THEREFORE` Total kinetic energy `=(1)/(2)mv^(2)+(1)/(2).(2)/(5)mR^(2).(v^(2))/(R^(2))` `=(1)/(2)mv^(2)+(1)/(5)mv^(2)` `=(7)/(10)mv^(2)` Putting `m=1kg, v=1m//s` Total energy `=(7)/(10)xx1xx(1)^(2)` `=(7)/(10)J`