Relativistic mass variation is given by m = m 0 I - v 2 c 2

The relativistic mass is the sum total quantity of energy in a body or system. Thus, the mass in the formula: E = m 0 c 2 is the relativistic mass. For a particle of finite rest mass m moving at a speed v relative to the observer, one finds m r e l = m 1 - v 2 c 2 In the centre of momentum frame, v = 0 and the relativistic mass equals the rest mass. In other frames, the relativistic mass (of a body or system of bodies) includes a contribution from the "net" kinetic energy of the body (the kinetic energy of the centre of mass of the body), and is larger the faster the body moves. Thus, unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. However, for given single frames of reference and for isolated systems, the relativistic mass is also a conserved quantity.

A rod of proper length l 0 moving with a speed v appears to have length l given as l = l 0 1 - v 2 c 2 . Is the given equation correct, if not give correct form.

The deviation between the measurements in all inertial frames is given by the formulas for Lorentz transformation and time dilation. It turns out that the proper length remains unchanged and always denotes the greatest length of an object, and the length of the same object measured in another inertial reference frame is shorter than the proper length. This contraction only occurs along the line of motion, and can be represented by the relation: l = l 0 γ v where l is the length observed by an observer in motion relative to the object l 0 is the proper length (the length of the object in its rest frame) γ v is the Lorentz factor, defined as γ v = 1 1 - v 2 c 2 where, v is the relative velocity between the observer and the moving object c is the speed of light Replacing the Lorentz factor in the original formula leads to the relation l = l 0 1 - v 2 c 2