A 3.0 gg particle has momentum 5.0×105 kg⋅m/skg⋅m/s What is the particle's speed?
Relativistic Momentum of a particle is given by:
P = *m*V
V = Speed of particle = ?
= Lorentz factor = 1/sqrt (1 - (V/c)^2)
m = mass of particle = 3.0 gm = 3.0*10^-3 kg
P = Momentum = 5.0*10^5 kg.m/sec
So,
P = m*V/sqrt (1 - (V/c)^2)
1 - (V/c)^2 = (m*V/P)^2
(V/c)^2 + (m*V/P)^2 = 1
V^2 = 1/(1/c^2 + m^2/P^2)
V = sqrt (1/(1/c^2 + m^2/P^2))
V = sqrt (1/(1/(3.00*10^8)^2 + (3.0*10^-3)^2/(5.0*10^5)^2))
V = 1.457*10^8 m/s = speed of particle
Let me know if you've any query.
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