A man pulls a solid cylinder `(` initially at rest `)` horizontal by a massless string. The string is wrapped on the cylinder and the cylinder performs pure rolling. Mass of the cylinder is `100kg`, radius is `pi` metre `&` tension in string is `100N`. Then the angular speed of the cylinder after one revolution will be `:`

Options

A. `4 rad //sec`
B. `(4)/ (sqrt(3)) rad//sec`
C. `(4)/(3) rad //sec`
D. non of these

Answer

B

Explanation

The cylinder rolls without slipping, hence no work is being doen by friction. In one complete revolution the centre `C` of the cylinder moves by `2pi R (R` is radius of cylinder `)` and the top most point `P` of the cylinder moves by `4 pi R`.

`v_(cm)=Romega (` from constraint `)`
Applying work energy theorem
Work done by `T=` increase in kinetic energy of cylinder
`Txx4 pi R=(1)/(2) I_(cm) omega^(2)+(1)/(2) mv_(cm)^(2)=(1)/(2)((1)/(2) mR^(2)) omega^(2)+(1)/(2) mR^(2) omega^(2)`
solving we get `omega =(4)/(sqrt(3)) rad //sec`