is2A wedge of mass M fitted with a spring of stiftness k is kept on a smoth hrizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all the surfaces are smooth, the potential energy stored in the spring:

a) mg2tan2θ/2k b) m2g tan2θ/2k c) m2g2tan2θ/2k d) m2g2tan2θ/k

To determine the potential energy stored in the spring, we need to first analyze the forces acting on the system and the equilibrium condition.

Let's consider the forces acting on the wedge. We have the weight force (mg) acting vertically downward and the normal force (N) acting perpendicular to the surface. There is no net force acting horizontally since the surface is smooth.

Now, let's analyze the forces acting on the rod. We have the weight force (mg) acting vertically downward, the normal force (N') acting perpendicular to the surface of the wedge, and the force due to the spring (Fs) acting horizontally towards the left. Again, there is no net force acting vertically since the surface is smooth.

Since the system is in equilibrium, the sum of forces in both the horizontal and vertical directions should be zero.

In the horizontal direction:
Fs = m * a
where a is the acceleration of the system

Since the system is in equilibrium, the acceleration (a) is zero. Therefore, the force due to the spring (Fs) is also zero.

Now, we can determine the potential energy stored in the spring.

The potential energy (PE) stored in a spring can be calculated using the formula:
PE = (1/2) * k * x^2
where k is the stiffness of the spring and x is the displacement from the equilibrium position.

In this case, the displacement (x) is zero because the force due to the spring (Fs) is zero. Therefore, the potential energy stored in the spring is also zero.

Hence, the correct option is (a) mg2tan2θ/2k, as it represents zero potential energy stored in the spring.