Question

An object has a relativistic momentum that is 8.30 times greater than its classical momentum. What is its speed?

Answer 1

Answer:

v = .992 c.

Explanation:

In relativistic mechanics , momentum

$mv=\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2} } }$

c is velocity of light  , m₀ is rest mass and v is velocity of the body..

Given

$\frac{mv}{m_0v} = 8.3$

$\sqrt{1 -\frac{v^2}{c^2} } = \frac{1}{8.3}$

Solving for v

v = .992 c.

Answer 2

Answer:

Speed of the object, v = 0.99 c

Explanation:

It is given that, an object has a relativistic momentum that is 8.30 times greater than its classical momentum.

The relativistic momentum is given by, $p=\dfrac{m_ov}{\sqrt{1-\dfrac{v^2}{c^2}}}$

Classical momentum, p' = mv

According to the given condition,

p = 8.3 p'

$\dfrac{m_ov}{\sqrt{1-\dfrac{v^2}{c^2}}}=8.3\times m_ov$

$\sqrt{1-\dfrac{v^2}{c^2}}=\dfrac{1}{8.3}$

$1-\dfrac{v^2}{c^2}=0.01451$

$\dfrac{v^2}{c^2}=0.985$

$v=0.99c$, c is the speed of light

So, the speed of the object is 0.99 c. Hence, this is the required solution.