Chapter 26, Problem 16P

To determine

The speed of an object.

Answer to Problem 16P

  $0.866c$ .

Explanation of Solution

Given:

An objects relativistic mass be twice of its rest mass.

Formula used:

It is known that,

  $m=\frac{m_0}{{\left[1-{\left(\frac{v}{c}\right)}^2\right]}^{\frac{1}{2}}}$

Where,

  $m_0$ is rest mass

  $m$ is relativistic mass

  $v$ is velocity

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

Calculation:

Substitute the given values in the formula $m=\frac{m_0}{{\left[1-{\left(\frac{v}{c}\right)}^2\right]}^{\frac{1}{2}}}$

  $2m_0=\frac{m_0}{{\left[1-{\left(\frac{v}{c}\right)}^2\right]}^{\frac{1}{2}}}$

  $v=0.866c$

Conclusion: The required value is $0.866c$ .