A uniform solid cylinder of mass M and radius R is free to rotate on frictionless horizontal axle, as shown in figure. Two masses, m each, hung from two cords wrapped around the cylinder. If the system is released from rest, the tension in each cord will be

Options

A. `(Mmg)/((4m+M))`
B. `(Mmg)/((2m+M))`
C. `(2Mmg)/((2m+M))`
D. `(2Mmg)/((4m+M))`

Answer

A

Explanation

The equation of motion of the system.
`2mg-2T=2ma or T + ma= mg .......(i) " " :. ` Torque ,`tau = Ialpha`
`:. RxxF=((MR^2)/2)a/R" or " a = (2F)/M=(2xx2T)/M=(4T)/M" ".....(ii)`
From (i) and (ii), we get,
`T+mxx(4T)/(M)=mg " or " T [1+(4m)/M]= mg " or " T= (Mmg)/(M+4m)`