JEE Advanced · Physics · 28. Nuclear Physics

A heavy nucleus $N$ , at rest, undergoes fission $N \to P + Q,$ where $P$ and $Q$ are two lighter nuclei. Let $δ = M_{N} - M_{P} - M_{Q}$ , where $M_{P}, M_{Q}$ and $M_{N}$ are the masses of $P, Q$ and $N$ , respectively. $E_{P}$ and $E_{Q}$ are the kinetic energies of $P$ and $Q$ , respectively. The speeds of $P$ and $Q$ are $v_{P}$ and $v_{Q}$ , respectively. If $c$ is the speed of light, which of the following statement(s) is (are) correct?

A $E_{P} + E_{Q} = c^{2} δ$
B $E_{P} = (\frac{M_{P}}{M_{P} + M_{Q}}) c^{2} δ$
C $\frac{v_{P}}{v_{Q}} = \frac{M_{Q}}{M_{P}}$
D The magnitude of momentum for $P$ as well as $Q$ is $c \sqrt{2 μ δ}$ , where $μ = \frac{M_{P} M_{Q}}{(M_{P} + M_{Q})}$

Verified Solution

Answer & Solution

Correct Answer

(A) $E_{P} + E_{Q} = c^{2} δ$

Step-by-step Solution

Detailed explanation

Since,

F_{e x t} = 0

So,

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

A rocket is moving in a gravity free space with a constant acceleration of $2 m s^{- 2}$ along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of $0.3 m s^{- 1}$ relative to the rocket. At the same time, another ball is thrown in - x direction with a speed of $0.2 m s^{- 1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other for the first time is

JEE Advanced 2014 Medium

A charged particle is introduced at the origin

x = 0, y = 0, z = 0

with a given initial velocity

\vec{v}

. A uniform electric field

\vec{E}

and a uniform magnetic field

\vec{B}

exist everywhere. The velocity

\vec{v}

, electric field

\vec{E}

and a uniform magnetic field

\vec{B}

are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(i) $\vec{E} = E_{0} \hat{z}$	(P) $\vec{B} = - B_{0} \hat{x}$
2. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{y}$	(ii) $\vec{E} = - E_{0} \hat{y}$	(Q) $\vec{B} = B_{0} \hat{x}$
3.Proton with $\vec{v}$ =0	(iii) $\vec{E} = {- E}_{0} \hat{x}$	(R) $\vec{B} = - B_{0} \hat{y}$
4. Proton with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(iv) $\vec{E} = E_{0} \hat{x}$	(S) $\vec{B} = - B_{0} \hat{z}$

In which case will the particle describe a helical path with axis along positive z direction?

JEE Advanced 2017 Medium

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