in figure the cylinder of mass `10kg` and radius 10 cm has a tape wrapped round it. The pully weighs 100 N and has a radius 5 cm. When the system is released the 5 kg mass comes down and the cylinder rolls without slipping. Calculate the acceleration and velocity of the mass as a function of time.

Explanation

Writing equations of motion we get
`5g-T_(2)=5a_(2)` ..(i)
`((T_(2)T_(1))R_(2))/((1)/(2)M_(2)R_(2)^(2))=alpha_(2)` ..(ii)
`T_(1)+f=M_(1)a_(1)` ..(iii)
`((T_(1)-f)R_(1))/((1)/(2)M_(1)R_(1)^(2))=alpha_(1)` ..(iv)
`a_(1)=R_(1)alpha_(1)` ..(v)
`a_(1)+R_(1)alpha_(1)=R_(2)alpha_(2)` .. (vi)
`R_(2)alpha_(2)=a_(2)` ..(vii)
We have seven unknows, `T_(1),T_(2),a_(1),a_(2),alpha_(1),alpha_(2)` and `f` solving above equations we get
`a_(2)=(4)/(11)g=3.6m//s^(2)`
`v=a_(2)t=(4gt)/(11)`