In the presented research work, we have solved a new kind of problem of forced shock waves in a compressible inviscid perfect gas having dirty (dust) particles of small size in a one-dimensional unsteady adiabatic flow. The approach, which we have used, is referred to as generalized geometry approach. Here we investigated how the density of the zone, which is undisturbed, changes as a function of the position from the point of the source of explosion. In addition, we have obtained an analytically a novel solution to the problem in the form of a new rule of power of time and distance. Further, we have investigated the energy behaviour of forced shock waves and interaction within the environment containing dust particles. Also, the behaviour of the entire energy of a forced shock wave is expounded at different Mach numbers, respectively, for planar geometry, cylindrically symmetric geometry, and spherically symmetric geometry under a dusty gas medium. Furthermore, the findings show that dust particles in a gas produce a more sophisticated representation rather than the standard gas dynamics.