Question

A rod bent in right angle along its centre line, is placed on a rough horizontal fixed cylinder of radius $R$ as shown in fig. Mass of rod is $2m$ and rod is in equilibrium. Assume that friction force on rod at $A$ and $B$ are equal in magnitude

• A. Normal force applied by cylinder on rod at $A$ is $3mg/2$
• B. Normal force applied by cylinder on rod at $B$ must be zero
• C. Friction force acting on rod at $B$ is upward
• D. Normal force applied by cylinder on rod at $A$ is mg

Answer 1

Answer: (A), (C)

The correct options are
A Normal force applied by cylinder on rod at $A$ is $3mg/2$
C Friction force acting on rod at $B$ is upward

The cylinder is fixed. Now let us observe rod A and B separately.

Forces on A are: $mg,f,N_A,N_{link}$.

Forces on B are: $mg,f,N_B,N_{link}$.

Since stationary, there is angular equilibrium from any point. Lets take the axis as centre of cylinder. If both $f$ are oppositely oriented, then unstable, hence both must be having same angular direction, i.e, opposite to mg(B). $2\ast f\ast R=mg\ast R=>f=mg/2$

But since, the system is stable linearly also, Fnet(A) = 0. Fnet(B) = 0.

Thus, $N_{link}=mg/2$ (pulling B upwards and A downwards). $N_b=0$ since there is no force perp. to the rod.

Therefore, $N_A=3mg/2$.