A circular ring of mass 10 kg rolls along a horizontal floor. The center of mass of the ring has a speed `1.5 m//s.` The work required to stop the ring is

Options

A. `10 J`
B. `-6J`
C. `14.5J`
D. `-22.5J`

Answer

D

Explanation

Given,
A circular ring rolls along a horizontal floor.
mass of ring, `m = 10 kg `
Speed of centre of mass of ring, `u = 1.5 m//s `
The work required to stop the ring is given by,
W = Final K.E-Initial K.E
`=K.E_(f) -K.E_(i)`
`=0- K.E_(i)`
`=K.E_(1)`
`=- (K.E_("rotational"+ K.E_("Linear"))`
` =- ((1)/(2) I omega ^(2) + (1)/(2) mv ^(2))`
`=- ((1)/(2) mR ^(2) ((V)/(R)) ^(2) + (1)/(2) mv ^(2)) (because I = mR^(2), w = (V)/(R))`
`=- ((1)/(2) mv ^(2) + (1)/(2) mv ^(2))`
`=- mv ^(2) `
`=- 10 xx (1.5) ^(2)`
`therefore W =- 22.5J`