A horizontal uniform rod of mass `'m'` has its left end hinged to the fixed incline plane, while its right end rrests on the top of a uniform cylinder of mass `'m'` which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest.

The ratio of magnitude of frictional force on the cylinder due to the rod and the magnitude of frictional force on the cylinder due to the inclined plane is `:`

Options

A. `1:1`
B. `2:sqrt(3)`
C. `2:1`
D. `sqrt(2):1`

Answer

A

Explanation

FBD of rod and cylinder is as shown.

Net torque on rod about hinge `'O'=0`
`:.N_(1)xxL=mgxx(L)/(2) or `
`N_(1) = (mg)/(2)`
Net torque on cylinder about its centre `C` is zero `:`
`f_(1)R=f_(2)R` or`f_(1) = f_(2)`
Net torque on cylinder about hinge `O` is zero.
`:. N_(2)xxL=N_(1)xxL+mgL`
or `N_(2)= ` , `(3mg)/(2)`