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A nucleus of mass M+ m is at rest and decays into two daughter

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A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $M /2$ each. Speed of light is c.

The speed of daughter nuclei is
(a) $c \frac{Δ m}{M + Δ m}$
(b) $c \frac{2Δ m}{M}$
(c) $c \frac{Δ m}{M}$
(d) $c \frac{Δ m}{M + Δ m}$

Views: 5,698 students

Updated on: Apr 10, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2010

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Lucas Discussed

A nucleus of mass

M + Δ m

is at rest and decays into two daughter nuclei of equal mass

M /2

each. Speed of light is c.

The speed of daughter nuclei is
(a)

c \frac{Δ m}{M + Δ m}

(b)

c \frac{2Δ m}{M}

(c)

c \frac{Δ m}{M}

(d)

c \frac{Δ m}{M + Δ m}

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Exp. (b)
By conservation of momentum,

0 = \frac{M}{2} v_{1} - \frac{M}{2} v_{2}

v_{1} = v_{2}

Δ m c^{2} = \frac{1}{2} \cdot \frac{M}{2} v_{1}^{2} + \frac{1}{2} \cdot \frac{M}{2} \cdot v_{2}^{2}

Δ m c^{2} = \frac{M}{2} v_{1}^{2}

\frac{2Δ m c ^{2}}{M} = v_{1}^{2} \Rightarrow v_{1} = c \frac{2Δ m}{M}

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Question Text	A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $M /2$ each. Speed of light is c. The speed of daughter nuclei is (a) $c \frac{Δ m}{M + Δ m}$ (b) $c \frac{2Δ m}{M}$ (c) $c \frac{Δ m}{M}$ (d) $c \frac{Δ m}{M + Δ m}$
Updated On	Apr 10, 2023
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	417
Avg. Video Duration	6 min

A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $M /2$ each. Speed of light is c.

The speed of daughter nuclei is
(a) $c \frac{Δ m}{M + Δ m}$
(b) $c \frac{2Δ m}{M}$
(c) $c \frac{Δ m}{M}$
(d) $c \frac{Δ m}{M + Δ m}$

Text solutionVerified

Filo tutor solutions (3)

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Text solutionVerified

Filo tutor solutions (3)

Questions from JEE Mains 2010 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

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A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $M /2$ each. Speed of light is c.

The speed of daughter nuclei is
(a) $c \frac{Δ m}{M + Δ m}$
(b) $c \frac{2Δ m}{M}$
(c) $c \frac{Δ m}{M}$
(d) $c \frac{Δ m}{M + Δ m}$