Istiak
- 158
- 12
- Homework Statement
- A particle of mass M at rest decays into two particles of masses m1 and m2 travelling in
opposite directions at velocity v1 and v2 respectively. Express v2 in terms of v1, m1, m2, and M.
- Relevant Equations
- ##m=\frac{m_0}{\sqrt{1-(\frac{v}{c})^2}}##
> A particle of mass M at rest decays into two particles of masses m1 and m2 traveling in opposite directions at velocity v1 and v2 respectively. Express v2 in terms of v1, m1, m2, and M.
Since both objects are from a single object that's why I took relativistic mass of both objects are same. I was thinking if there's some other simple equation to solve this but I couldn't find it.
##\frac{m_2}{\sqrt{1-(\frac{v_2}{c})^2}}=\frac{m_1}{\sqrt{1-(\frac{v_1}{c})^2}}##
After rearranging the equation I get
##\frac{m_2}{m_1}=\frac{\sqrt{c^2-v_2^2}}{\sqrt{c^2-v_1^2}}##
But that's not the correct answer. So what's the correct one? What the concept should be to solve the question?
Since both objects are from a single object that's why I took relativistic mass of both objects are same. I was thinking if there's some other simple equation to solve this but I couldn't find it.
##\frac{m_2}{\sqrt{1-(\frac{v_2}{c})^2}}=\frac{m_1}{\sqrt{1-(\frac{v_1}{c})^2}}##
After rearranging the equation I get
##\frac{m_2}{m_1}=\frac{\sqrt{c^2-v_2^2}}{\sqrt{c^2-v_1^2}}##
But that's not the correct answer. So what's the correct one? What the concept should be to solve the question?
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