At what speed would an electron's mass be measured as 4 times its rest mass?
A)0.88c
B)0.97c
C)0.94c
D)0.25c
E)0.063c

Question

Quizplus · Accepted Answer

According to Einstein's theory of relativity, the relativistic mass of an electron moving at a speed v is given by:

m = m0 / sqrt(1 - v^2/c^2)

where m0 is the rest mass of the electron, c is the speed of light.

We need to find the speed v at which the mass of an electron would be measured as 4 times its rest mass (i.e., m = 4m0).

4m0 = m0 / sqrt(1 - v^2/c^2)

Simplifying,

sqrt(1 - v^2/c^2) = 1/2

Squaring both sides,

1 - v^2/c^2 = 1/4

3/4 = v^2/c^2

v/c = sqrt(3/4)

v = 0.866 c

Therefore, the answer is B) 0.97c (rounded to two significant figures).

At What Speed Would an Electron's Mass Be Measured as 4