The speed at which a particle's relativistic momentum equal twice its classical momentum, will be 2.598* 10^8 m/s.
Relativistic momentum ensures that the conservation of momentum holds in all inertial frames.
The relativistic effects of length contraction, time dilation, and other similar phenomena are experienced by particles when they move at very high speeds (near the speed of light). The mass of the particles also varies at this high speed. The relativistic momentum is the product of the particle's velocity and its corresponding relativistic mass.
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Classical momentum P(c)= m'v (m' is the mass of the particles at rest and v is its speed) ..........(1)
Relativistic momentum P(r)= mv ....(2)
Now, P(r)= 2P(c) ....(3)
Relativistic mass m= γm' ( γ is the Lorenz factor) ....(4)
γ= γ 1/ (√1−((v^2)/c^2)))
Putting the value of m' from equation 1 in 4 and then simplifying it, we will get the value of
v= (√3/2) *c
Putting c as the speed of light = 3* 10^8 m/s
v= 2.598* 10^8 m/s
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