A particle is moving at 0.86c.By what magnitude percentage is the Newtonian expression for momentum in error? (The percentage error is the difference between the erroneous and correct expressions,relative the correct one).
A)49%
B)40%
C)55%
D)62%

Question

Quizplus · Accepted Answer

The correct expression for momentum at relativistic speeds is given by:

p = mv/√(1 - v^2/c^2)

where m is the mass, v is the velocity, and c is the speed of light.

The Newtonian expression, which is valid only for non-relativistic speeds, is given by:

p = mv

Now, we can find the percentage error in the Newtonian expression by comparing it to the correct expression:

error = [(p_correct - p_newtonian)/p_correct] * 100

Substituting the values given,

v = 0.86c

we get

p_correct = mv/√(1 - v^2/c^2) = m(0.86c)/√(1 - 0.86^2) = 2.54m

p_newtonian = mv = 0.86mc = 0.86p_correct

Putting it in the above error expression, we get

error = [(p_correct - 0.86p_correct)/p_correct] * 100 = 0.14 * 100 = 14%

So, the magnitude percentage error in the Newtonian expression is:

error = 100% - 14% = 86%

Therefore, Option A is correct.

A Particle Is Moving at 0