Correct option is (4) \(\frac 1{12}\) kg
All the forces acting on the rod are as shown in the figure below:
For the rod to remain in equilibrium,
τnet = 0
Calculating the net torque about the wedge, we have:
2g × 20 = 0.5g × 60 + mg × 120
m = \(\frac{0.5}6\) kg = \(\frac 1{12}\) kg