A nucleus moving with a velocity v - emits an -particle- Let the velocities of the -particle and the remaining nucleus be v1 and v2 and their masses bem1 and m2a v - v - 1 and v - 2 must be parallel to each other-b None of the two of v - v - 1 and v - 2 should be parallel to each other-c v 1 - v 2 - must be parallel to v -d m 1 v 1 - m 2 v 2 - must be parallel to v -

(d) m1v1 #8594;+m2v2 #8594; must be parallel to v #8594; By the law of conservation of linear momentum, we can write: nbsp;Initial #160;momentum ...

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Byju's Answer

Standard IX

Physics

Conservation of Momentum

A nucleus mov...

Question

A nucleus moving with a velocity $\vec{v}$ emits an α-particle. Let the velocities of the α-particle and the remaining nucleus be v₁ and v₂ and their masses be m₁ and m₂.
(a) $\vec{v}, {\vec{v}}_{1} and {\vec{v}}_{2}$ must be parallel to each other.
(b) None of the two of $\vec{v}, {\vec{v}}_{1} and {\vec{v}}_{2}$ should be parallel to each other.
(c) $\vec{v_{1}} + \vec{v_{2}}$ must be parallel to $\vec{v}$
(d) $m_{1} \vec{v_{1}} + m_{2} \vec{v_{2}}$ must be parallel to $\vec{v}$

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Solution

(d) $m_{1} \vec{v_{1}} + m_{2} \vec{v_{2}}$ must be parallel to $\vec{v}$

By the law of conservation of linear momentum, we can write:

$Initial momentum = Final momentum \Rightarrow m \vec{v} = m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2} \Rightarrow (m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}) must be parallel to \vec{v}$

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(d) m1v1→+m2v2→ must be parallel to v→ By the law of conservation of linear momentum, we can write: Initial momentum = Final momentum⇒mv→ = m1v→1 + m2v→2⇒(m1v→1 + m2v→2) must be parallel to v→