Question

proton is accelerated to a speed of 0.93c, what is the 1. A proton has a mass of 1.673 x 10-27 kg. If the proton is accelerated to a speed magnitude of the relativistic momentum of the proton? A. 6.2 x 10-17 kg. m/s B. 1.3 x 10-18 kg. m/s C. 4.7 x 10-19 kg. m/s D. 5.9 x 10-24 kg. m/s E. 1.8 * 10-18 kg . m/s

Answer 1

Answer : The correct option is, (B)
`1.3* 10^(-18)kg.m/s`

Explanation : Given,

Mass of proton =
`1.673* 10^(-27)kg`

Speed of proton = 0.93 c

Formula used for relativistic momentum of the proton is:

`p=\frac{m_ov}{\sqrt{1-(v^2)/(c^2)}}`

where,

p = relativistic momentum of the proton

`m_o` = mass of proton

v = speed of proton

c = speed of light =
`3* 10^8m/s`

Now put all the given values in the above formula, we get:

`p=\frac{(1.673* 10^(-27)kg)* (0.93c)}{\sqrt{1-((0.93c)^2)/(c^2)}}`

`p=((1.55589* 10^(-27)c))/(0.367)`

`p=((1.55589* 10^(-27))* (3* 10^8))/(0.367)`

`p=1.272* 10^(-18)kg.m/s\approx 1.3* 10^(-18)kg.m/s`

Therefore, the relativistic momentum of the proton is,
`1.3* 10^(-18)kg.m/s`