The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load P > 0 with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are

The correct option is BF and DH only.

To determine the zero-force members in the given truss, we apply the principles of static equilibrium at the joints (Method of Joints). Specifically, we use the standard rule for identifying zero-force members at three-member joints:
Rule: If three members meet at a joint where no external load or support reaction is applied, and two of the members are collinear, then the third (non-collinear) member must be a zero-force member.

Let us analyze the joints of the truss using the details provided in the diagram:

1. Analysis of Joint B:
At Joint B, three members meet: AB, BC, and BF. Looking at the horizontal bottom chord of the truss, members AB and BC are collinear along the horizontal axis. The vertical member BF is perpendicular (non-collinear) to them. Since there is no external load acting at joint B and there is no support support reaction at this joint, the equilibrium equation in the vertical direction (perpendicular to the collinear members) gives:

$$\sum F_y=0\Rightarrow F_{\mathrm{BF}}=0$$

Therefore, member BF is a zero-force member.

2. Analysis of Joint D:
Similarly, at Joint D, three members meet: CD, DE, and DH. The members CD and DE are collinear along the horizontal bottom chord of the truss. The vertical member DH is perpendicular to them. Since there is no external load or reaction force acting at joint D, the equilibrium equation in the vertical direction gives:

$$\sum F_y=0\Rightarrow F_{\mathrm{DH}}=0$$

Therefore, member DH is a zero-force member.

Hence, the members carrying zero force are BF and DH only.