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

Correct answer: B. c (2 Δ m)/(M) Conserving the momentum gathered 0= M 2 ~V_1- M 2 ~V_2 ~V_1=V_2 (1) Δ mc^2=(1)/(2) · M 2 ~V_1^2+(1)/(2) · M 2 · V_2^2 (2) Δ mc^2= M 2 ~V_1^2 2 Δ mc^2 M =V_1^2 ~V_1=c 2 Δ m M gathered

JEE Main 2010

Exam: JEE Main
Year: 2010
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2010 · Physics · Nuclear Physics

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

A nucleus of mass

M+\Delta m

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

\frac{M}{2}

each. Speed of light is

\mathrm{C}

. The speed of daughter nuclei is

Options

A $c \frac{\Delta m}{M+\Delta m}$
B $c \sqrt{\frac{2 \Delta m}{M}}$
C $c \sqrt{\frac{\Delta \mathrm{m}}{\mathrm{M}}}$
D $c \sqrt{\frac{\Delta m}{M+\Delta m}}$

Correct answer

B. $c \sqrt{\frac{2 \Delta m}{M}}$

Step-by-step solution

Conserving the momentum

\begin{gathered} 0=\frac{\mathrm{M}}{2} \mathrm{~V}_1-\frac{\mathrm{M}}{2} \mathrm{~V}_2 \\ \mathrm{~V}_1=\mathrm{V}_2 \quad \quad \ldots \ldots (1) \\ \Delta \mathrm{mc}^2=\frac{1}{2} \cdot \frac{\mathrm{M}}{2} \mathrm{~V}_1^2+\frac{1}{2} \cdot \frac{\mathrm{M}}{2} \cdot \mathrm{V}_2^2 \quad \quad \ldots \ldots (2)\\ \Delta \mathrm{mc}^2=\frac{\mathrm{M}}{2} \mathrm{~V}_1^2 \\ \frac{2 \Delta \mathrm{mc}^2}{\mathrm{M}}=\mathrm{V}_1^2 \\ \mathrm{~V}_1=\mathrm{c} \sqrt{\frac{2 \Delta \mathrm{m}}{\mathrm{M}}} \end{gathered}

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