Final answer:
The dimension analysis of the equation p = V2 m Elt reveals that the equation is not dimensionally correct for representing momentum, since the dimensions on the left side (kg·m/s) do not match the dimensions on the right side (kg·m²/s³).
Step-by-step explanation:
To check the correctness of the given expression for the momentum (p) of a body of mass (m) with total energy (E) and considering the duration of time (t) as p = V2 m Elt, we need to conduct dimensional analysis. Linear momentum is defined as the product of a system's mass multiplied by its velocity. It is expressed as p = mv, where m is the mass and v is the velocity. The SI unit for momentum is kg·m/s.
The total energy (E) for a particle can be represented as E = mc² if we're considering the rest mass, or E = ymc² with a relativistic correction for velocity. In any case, the units for energy are kg·m²/s².
Dimensional analysis requires that both sides of the equation have the same dimensions. In this case, we expect the dimensions of momentum (kg·m/s) to be equal to the expression provided. However, the given expression includes an additional term of energy (E), and time (t), which gives it dimensions of kg·m²/s³ when using E = ymc². Therefore, the dimensional analysis does not verify the equation p = V2 m Elt as being correct for momentum.