A body of rest mass $m_{0}$ collides perfectly inelastically at a speed of 0.8c with another body of equal rest mass kept at rest. Calculate the common speed of the bodies after the collision and the rest mass of the combined body.

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Solution

Given: $m a s s = m_{0}, v_{1} = 0.8 c$
We know,
(mass of body 1)(initial Velocity of body 1)+(mass of body 2)(initital velocity of body 2)
=(mass of 1+mass of 2)(final combined velocity)
$\Rightarrow m_{1} u_{1} + m_{2} u_{2} = (m_{1} + m_{2}) v_{f} \Rightarrow v_{f} = \frac{m_{0} u_{1} + 0}{m_{0} + m_{0}} = \frac{(m_{0}) (0.8 c)}{2 m_{0}} = 0.4 c$
Common speed of the bodies is $0.4 c$
And the combined mass will be $2 m_{0}$

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A body of rest mass m0 collides perfectly inelastically at a speed of 0.8c with another body of equal rest mass kept at rest. Calculate the common speed of the bodies after the collision and the rest mass of the combined body.

Given: mass=m0,v1=0.8cWe know, (mass of body 1)(initial Velocity of body 1)+(mass of body 2)(initital velocity of body 2) =(mass of 1+mass of 2)(final combined velocity)⇒m1u1+m2u2=(m1+m2)vf⇒vf=m0u1+0m0+m0=(m0)(0.8c)2m0=0.4cCommon speed of the bodies is 0.4cAnd the combined mass will be 2m0

A body of rest mass $m_{0}$ collides perfectly inelastically at a speed of 0.8c with another body of equal rest mass kept at rest. Calculate the common speed of the bodies after the collision and the rest mass of the combined body.