Question

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

Answer 1

v = .992 c.

Step-by-step explanation:

In relativistic mechanics , momentum

`mv=\frac{m_0v}{\sqrt{1-(v^2)/(c^2) } }`

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

Given

`(mv)/(m_0v) = 8.3`

`\sqrt{1 -(v^2)/(c^2) } = (1)/(8.3)`

Solving for v

v = .992 c.

Answer 2

Speed of the object, v = 0.99 c

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

Classical momentum, p' = mv

According to the given condition,

p = 8.3 p'

`\frac{m_ov}{\sqrt{1-(v^2)/(c^2)}}=8.3* m_ov`

`\sqrt{1-(v^2)/(c^2)}=(1)/(8.3)`

`1-(v^2)/(c^2)=0.01451`

`(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.