Answer to Question #292351 in Mechanics | Relativity for koushik

Question

a body quadruples its momentum when its speed doubles what was the initial speed as fraction of c of the body

Answer 1

Explanations & Calculations

• Here relativistic momentum needs to be considered.

$\qquad\qquad \begin{aligned} \small P&\to \small 4P\\ \small m& \to \small 2m\\ \\ \small P_{relativistic}&=\small \gamma.m.v\\ \small P&=\small \frac{1}{\sqrt{1-\large\frac{v^2}{c^2}}}.m.v\quad\cdots(1)\\ \small 4P&=\small \frac{m(2v)}{\sqrt{1-\large\frac{4v^2}{c^2}}}\quad\cdots(2)\\ \\ (1)\div(2),\\ \\ \small \frac{v}{c}&=\small 0.447 \end{aligned}$