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 magnitude of normal reaction exerted by the rod on the cylinder is

Options

A. `(mg)/(4)`
B. `(mg)/(3)`
C. `(mg)/(2)`
D. `(2mg)/(3)`

Answer

C

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)`