A cylinder is sandwiched between two planks. Two constant horizontal forces `F` and `2F` are applied on the planks as shown. Determine the acceleration of the centre of mass of cylinder and the top plank. If there is no slipping at the top and bottom of cylinder.

Explanation

Equation of motion are,
`F+f_(1)=Ma_(1)` ..(i)
`f_(1)+f_(2)=Ma_(2)` ..(ii)
`2F-f_(2)=2Ma_(3)`
`alpha=((f_(1)-f_(2))R)/((1)/(2)MR^(2))`
or `alpha=(2(f_(1)-f_(2)))/(MR)` ..(iv)
for no slipping condition,
`a_(2)+Ralpha=a_(1)` .(v)
and `a_(2)-Ralpha=a_(3)` .(vi)

we have six unknowns, `f_(1),f_(2),a_(1),a_(2),a_(3)` and `alpha`
Solving the above six equations we get
`a_(1)=(21F)/(26M)` and `a_(2)=(F)/(26M)`