A hoop of radius `2 m` weight `100 kg`.It rolls along a horizontal floor so that its centre of mass has a speed of `20 cm s^-1`. How much work has to be done to stop it ?

Explanation

Here, `R = 2m, M = 100 kg`
`v = 20 cm//s = (1)/(5)m//s, W =?`
Total energy `= (KE)_(T) + (KE)_(R)`
`=(1)/(2)M v^(2) + (1)/(2)I omega^(2)`
`=(1)/(2)M v^(2) + (1)/(2)(MR^(2))omega^(2)`
`=(1)/(2)M v^(2) + (1)/(2) M v^(2) = M v^(2)`
Work reqd. to be done = Total energy
`W = Mv^(2)`
`= 100 ((1)/(5))^(2) = 4J`