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A solid cylinder of mass M and radius 2R...

A solid cylinder of mass M and radius 2R is rolled up on an incline with the help of a plank of mass 2M as shown in the figure. A constant force F is acting on the plank parallel to the incline. There is no slipping at any of the contact. The friction force between the plank and cylinder is given by:

A

`F/2`

B

`(3F + 29 Mg sin theta)/57`

C

`(3F + 2Mg sin theta)/19`

D

Coefficient of friction value is not given and hence Cannot be found

Text Solution

Verified by Experts

The correct Answer is:
C
The free body diagram of the plank and the cylinder is as shown in the figure.
For plank, `F-f_(1)=2 Mg sin theta = 2 Ma_(1)`
For cylinder, `f_(1)-f_(2) = Mg sin theta = Ma_(2)`
`(f_(1) + f_(2))R =(MR^(2))/2 alpha`

For no slipping between plank and cylinder, `a_(2) = Ralpha = a_(1)`
For no slipping between cylinder and incline, `a_(2) = Ralpha`
After, solving the above equation, `f_(1) =(3F + 2Mg sin theta)/19`
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