A disc of mass 5 kg and radius 50 cm rolls on the ground at the rate of `10 ms^(-1)`. Calculate the K.E. of the disc.

Explanation

Given, mass of the disc, `M = 5 kg`
Radius of the disc, `R=50 "cm"=(1)/(2)m`
Linear velocity of the disc, `v=10 ms^(-1)`
`because v = R omega rArr 10 = (1)/(2) omega`
`rArr omega = 10 xx 2 =20 "rad s"^(-1)`
Also, moment of inertia pf disc about an axismk through its centre,
`I=(1)/(2)MR^(2)`
`rArr I=(1)/(2)xx5xx((1)/(2))^(2)=(5)/(8)"kg-m"^(2)`
`because` Kinetic enegry of translation `= (1)/(2) mv^(2)`
`=(1)/(2) xx5xx(10)^(2)=250 J`
`because` Kinetic energy of rotation `= (1)/(2) I omega^(2)`
`= (1)/(2)xx(5)/(8) xx(20)^(2)=125 J`
`:.` Total kinetic energy `- (250+125) J 375 J`.