A solid cylinder is sandwiched between two planks. Two constant horizontal forces F and 2F are applied on the planks as shown. Masses of planks and cylinder are indicated in the figure. Radius of the cylinder is R. Then

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the acceleration of the centre of mass of cylinder is towards right

the acceleration of the centre of mass of cylinder is towards left

frictional force on the upper plank is $\frac{5 F}{26}$

frictional force on the lower plank is $\frac{5 F}{26}$

answer is B, C.

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Detailed Solution

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Equations of motion are, $F + f_{1} = M a_{1}, f_{1} + f_{2} = M a_{2}$
$2 F - f_{2} = 2 M a_{3} α = \frac{(f_{1} - f_{2}) R}{\frac{1}{2} m R^{2}}$
For no slipping $a_{2} + R α = - a_{1}; a_{2} - R α = a_{3}$
Solving above equations we get $a_{1} = \frac{21 F}{26 M}$ and $a_{2} = \frac{F}{26 M} f_{1} = - \frac{5 F}{26}$