Question

A 3.0 gg particle has momentum 5.0×10⁵ kg⋅m/skg⋅m/s What is the particle's speed?

Answer 1

Relativistic Momentum of a particle is given by:

P = $\gamma$ *m*V

V = Speed of particle = ?

$\gamma$ = 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

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