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### The Various Equations of Variation of Mass with Velocity

#### Affiliations

• Fundamental Physics Society, His Mercy Enclave, Post Box 107 GPO Shimla – 171001, Himachal Pradesh, India

#### Abstract

Objectives: The origin of various equations involving variation of mass with velocity is discussed and new exponential equation is derived. At lower velocity this equation and Lorentz equation both give same results. Methods/Statistical Analysis: The various references right from inception of concept of variation of mass with velocity are discussed. The basic common point in various equations is that invalid operation division by zero is involved. Initially such equation was initiated by Thomson, and used by following scientists. Thus aspects are theoretically discussed. Findings: A newly derived equation is exponential in nature and is interpreted in view of existing experimental observations. It does not involve division by zero, hence never predicts that mass becomes infinite when velocity of body, v =c. Lorentz has given equation for transverse mass mT = ε 􀟛 mrest , where is undetermined factor or coefficient differing from unity by quantity of the order v2/c2. Lorentz’s equation (relativistic mass) is experimentally verified by with reasonable accuracy up to velocity 0.75c. Thus Lorentz’s equation is confirmed in limited region. In LHC the protons have energy 13TeV move with velocity at about 0.9999 99990c, at this velocity the relativistic mass of proton must be experimentally measured and compared. Then it must be confirmed up to which extent Lorentz’s equation is obeyed. New theory of variability of speed of light implies that speed of light was more in the early universe. It supports exponential equation which allows superluminal velocity. Applications/ Improvements: The exponential equation is the first equation which provides extension in the Lorentz equation in conceptual and mathematical way. It stresses superluminal velocities at some stages of formation of universe. The exponential equation can be checked in experiments in LHC which involve velocities tending to that of light and other experiments.

#### Keywords

Einstein, Exponential Equation, Lorentz, Relativistic Mass, Transverse Mass

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#### References

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