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A particle of...

Question

A particle of mass $m_{1}$ collides head on with another stationary particle of $m_{2}$ perfectly inelastically ( $m_{2} > m_{1}$ ). The fraction of kinetic energy which converted into heat in this collision is-

\frac{m_{2}}{m_{1} + m_{2}}

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\frac{m_{1}}{m_{1} + m_{2}}

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\frac{m_{1}}{m_{1} - m_{2}}

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\frac{m_{2}}{m_{1} - m_{2}}

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Solution

The correct option is A $\frac{m_{2}}{m_{1} + m_{2}}$
$0.5 m_{1} v_{1}^{2} = 0.5 (m_{1} + m_{2}) v_{C O M}^{2} + H e a t$
$P = m_{1} v_{1} = (m_{1} + m_{2}) v_{C O M}$
$H e a t = (P^{2} / 2) (1 / m_{1} - 1 / (m_{1} + m_{2})) = P^{2} m_{2} / 2 m_{1} (m_{1} + m_{2})$

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A particle of mass m1 collides head on with another stationary particle of m2 perfectly inelastically (m2>m1). The fraction of kinetic energy which converted into heat in this collision is-

The correct option is A m2m1+m20.5m1v21=0.5(m1+m2)v2COM+HeatP=m1v1=(m1+m2)vCOMHeat=(P2/2)(1/m1−1/(m1+m2))=P2m2/2m1(m1+m2)

A particle of mass $m_{1}$ collides head on with another stationary particle of $m_{2}$ perfectly inelastically ( $m_{2} > m_{1}$ ). The fraction of kinetic energy which converted into heat in this collision is-

The correct option is A $\frac{m_{2}}{m_{1} + m_{2}}$
$0.5 m_{1} v_{1}^{2} = 0.5 (m_{1} + m_{2}) v_{C O M}^{2} + H e a t$
$P = m_{1} v_{1} = (m_{1} + m_{2}) v_{C O M}$
$H e a t = (P^{2} / 2) (1 / m_{1} - 1 / (m_{1} + m_{2})) = P^{2} m_{2} / 2 m_{1} (m_{1} + m_{2})$