Question

A heavy meterstick has a mass of 1 kg. When the meterstick is thrown like a spear past you, you measure its momentum to be 2mv. What do you measure its length to be?

Answer 1

Its length is measured to be 0.5 m

Step-by-step explanation:

From theory of relativity (mass variation), we know that:

m = mo/√(1-v²/c²)

Where, m = relative mass

and, mo = rest mass

The momentum of stick while moving, will be:

P = mv

but, it is given in the form of rest mass as:

P = 2(mo)v

thus, by comparison;

2(mo)v = mv

using value of m from theory of relativity;

2(mo)v = (mo)v/√(1-v²/c²)

√(1-v²/c²) = 1/2 ______ eqn(1)

Now, for relativistic length (L), we have the formula from same theory of relativity;

L = (Lo)√(1-v²/c²)

The rest length (Lo) of meter stick is 1 m, and the remaining term on right side √(1-v²/c²), known as Lorentz Factor, can be given by eqn (1), as equal to 1/2.

Thus,

L = (1 m)(1/2)

L = 0.5 m