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  4. A particle of rest mass m0 is travelling so that its total energy is twice its rest mass energy. It collides with another stationary particle of rest mass m0 to form a new particle. What is the rest mass of the new particle?

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Q. A particle of rest mass $m_0$ is travelling so that its total energy is twice its rest mass energy. It collides with another stationary particle of rest mass $m_{0}$ to form a new particle. What is the rest mass of the new particle?

KEAMKEAM 2018Nuclei

Solution:

$\because$ Total energy of particle $=m c^{2}-m_{o} c^{2}$
rest mass energy of particle $=m_{0} c^{2}$
according question,
$\Rightarrow \,m c^{2}-m_{0} c^{2}=2 m_{0} c^{2}$
or $m=3 m_{0}$
When a particle collides with another particle
then net mass of new particle will be $m=3 m_{0}$