In the following problems, indicate the correct direction of friction force acting on the cylinder, which is pulled on a rough surface by a constant force `F`.
A cylinder is placed on a rough plank which in turn is placed on a smooth surface. The plank is pulled with a constant force `F`. The friction force can be given by which of the following diagrams.
.

Options

A.
B.
C.
D. cannot be interpreted

Answer

B

Explanation

Case I

`a_(P) = a + R alpha rArr a_(p) = (f)/(m) + R (tau)/(I)`
`a_(p) = (f)/(m) + (R^(2) f)/(I)` & `a_(p)' (F - f)/(m)`
fro pure rolling
`a_(p) = a_(p)'`
`(f)/(m) + (R^(2) f)/(I) = (F -f)/(m) rArr (F)/(m) = (2f)/(m) - (R^(2) f)/(I)`
`f = (F)/(2 + (mR^(2))/(I))`
Case II

`a_(p)' ne a_(p)`
so friction will be in forward direction on cylinder.