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- Center of Mass, Momentum and Collision
NEET · Physics · Center of Mass, Momentum and Collision
Particle of mass m, kinetic energy K and momentum P collides head...
Particle of mass m, kinetic energy K and momentum P collides head on elastically with another particle of mass 2 m at rest. After collision:
(
)
| Column I | Column II | ||
| (A) | Momentum of ^{st } particle | (P) | P |
| (B) | Momentum of II^{rd } particle | (Q) | |
| (C) | KE^{of } ^{sd } particle | (R) | |
| (D) | KE^{of } II^{rd } particle | (S) | - |
Options
- A(\mathrm{A} \rightarrow \mathrm{S} ; \mathrm{B} \rightarrow \mathrm{P}, \mathrm{C} \rightarrow \mathrm{Q}, \mathrm{D} \rightarrow \mathrm{R})
- B(\mathrm{A} \rightarrow \mathrm{P} ; \mathrm{B} \rightarrow \mathrm{S}, \mathrm{C} \rightarrow \mathrm{Q}, \mathrm{D} \rightarrow \mathrm{R})
- C(\mathrm{A} \rightarrow \mathrm{P} ; \mathrm{B} \rightarrow \mathrm{S}, \mathrm{C} \rightarrow \mathrm{R}, \mathrm{D} \rightarrow \mathrm{Q})
- D(\mathrm{A} \rightarrow \mathrm{S} ; \mathrm{B} \rightarrow \mathrm{P}, \mathrm{C} \rightarrow \mathrm{R}, \mathrm{D} \rightarrow \mathrm{Q})
Correct answer
A. (\mathrm{A} \rightarrow \mathrm{S} ; \mathrm{B} \rightarrow \mathrm{P}, \mathrm{C} \rightarrow \mathrm{Q}, \mathrm{D} \rightarrow \mathrm{R})
Step-by-step solution
(v_1 \& v_2) are velocities after collision Conservation of linear momentum
(\begin{gathered}
\mathrm{mu}=\mathrm{mv}_1+2 \mathrm{mv}_2 \\
\mathrm{u}=\mathrm{v}_1+\mathrm{v}_2 \quad \ldots (1) \\
\mathrm{e}=1=\frac{\mathrm{v}_2-\mathrm{v}_1}{\mathrm{u}} \\
\mathrm{u}=\mathrm{v}_2-\mathrm{v}_1 \quad \ldots (2)
\end{gathered})
From (1) & (2)
(v_2=\frac{2 u}{3} ; v_1=-\frac{u}{3})
Momentum of (1^{\text{t }}) particle (=-\frac{\mathrm{mu}}{3}=-\frac{\mathrm{P}}{3})
Momentum of (2^{\text{nd }}) particle (=+2 \mathrm{ m}\left(\frac{2 \mathrm{u}}{3}\right)=\frac{4 \mathrm{P}}{3})
K.E. of particle (=\frac{1}{2} \mathrm{ m}\left(\frac{\mathrm{u}}{3}\right)^2=\frac{\mathrm{K}}{9})
K.E. of (2^{\infty}) particle (=\frac{1}{2} \times 2 \mathrm{ m}\left(\frac{2 \mathrm{u}}{3}\right)^2=\frac{8 \mathrm{ K}}{9})