Nuclear charges non-uniformly | Physics | JEE Advance 2008

Competishun Header

JEE Advance 2008

Paper-2

Question

The nuclear charges (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ form the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

The electric field within the nucleus is generally observed to be linearly dependent on r . This implies

Select the correct option:

A

$\mathrm{a}=0$

B

$\mathrm{a}=\frac{\mathrm{R}}{2}$

C

$a=R$

D

$\mathrm{a}=\frac{2 \mathrm{R}}{3}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Advance

Physics

Easy

Start Preparing for JEE with Competishun

Video Solution

BY competishun

Watch Solution from 1:29:55

YouTube

Filters 0

Showing 18 questions

Solution A is prepared by dissolving 1 g of a protein (molar mass $=50000 \mathrm{~g} \mathrm{~mol}^{-1}$ ) in 0.5 L...

JEE MainPhysicsEasy

View Solution→

Gas ' $A$ ' undergoes change from state ' $X$ ' to state ' $Y$ '. In this process, the...

JEE MainPhysicsEasy

View Solution→

Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\} \rightarrow\left\{1, e, e^2, e^3\right\}$ and $...

JEE MainMathematicsMedium

View Solution→

\text { The area of the region }\left\{(x, y): 0 \leq y \leq 6-x, y^2 \geq 4 x-3, x \geq...

JEE MainMathematicsEasy

View Solution→

The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32 \cos ^4 x}{1+e^{\sin x}}\right) d x$ is:

JEE MainMathematicsMedium

View Solution→

QJEE MAIN 20262026

The area of the region $\left\{(x, y): 0 \leq y \leq 6-x, y^2 \geq 4 x-3, x \geq 0\right\}$ is:

JEE MainMathematicsEasy

View Solution→

QJEE MAIN 20262026

Let $f:[1, \infty) \rightarrow \mathbf{R}$ be a differentiable function defined as $f(x)=\int_1^x f(\mathrm{t}) \mathrm{dt}+(1-x)\left(\log _0 x-1\right)+\mathrm{e}$. Then the value of...

JEE MainMathematicsMedium

View Solution→

QJEE MAIN 20262026

The value of $\lim _{x \rightarrow 0}\left(\frac{x^2 \sin ^2 x}{x^2-\sin ^2 x}\right)$ is:

JEE MainMathematicsEasy

View Solution→

Let a line L be perpendicular to both the lines $\mathrm{L}_1: \frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $\mathrm{L}_2: \frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$. If $\theta$ is the acute...

JEE MainMathematicsEasy

View Solution→

QJEE MAIN 20262026

Let $\left(2^{1-a}+2^{1+a}\right), f(a),\left(3^a+3^{-a}\right)$ be in A.P. and $\alpha$ be the minimum value of $f(a)$. Then the value of the integral...

JEE MainMathematicsMedium

View Solution→

$\mathrm{SF}_4$ is isostructural with: A. $\mathrm{BrF}_4{ }^{!}$ B. $\mathrm{CH}_4$ C. $\mathrm{IF}_4^{\oplus}$ D. $\mathrm{XeF}_4$ E. $\mathrm{XeO}_2 \mathrm{~F}_2$ Choose the correct answer...

JEE MainPhysicsMedium

View Solution→

Let the image of the point $\mathrm{P}(1,6, a)$ in the line $\mathrm{L}: \frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0$, be $\left(\frac{a}{3}, 0, a+c\right)$. If $...

JEE MainMathematicsMedium

View Solution→

QJEE MAIN 20262026

Let $f(x)=\lim _{y \rightarrow 0} \frac{(1-\cos (x y)) \tan (x y)}{y^3}$. Then the number of solutions of the equation $...

JEE MainMathematicsMedium

View Solution→

QJEE MAIN 20262026

Let $S=\{\theta \in(-2 \pi, 2 \pi): \cos \theta+1=\sqrt{3} \sin \theta\}$. Then $\sum_{\theta \in S} \theta$ is equal to:

JEE MainMathematicsEasy

View Solution→

QJEE MAIN 20262026

Let $O$ be the origin, $\overrightarrow{O P}=\vec{a}$ and $\overrightarrow{O Q}=\vec{b}$. If $R$ is the point on $\overrightarrow{O P}$ such that...

JEE MainMathematicsEasy

View Solution→

The first and second ionization constants of a weak dibasic acid $\mathrm{H}_2 \mathrm{~A}$ are $8.1 \times 10^{-8}$ and $...

JEE MainPhysicsHard

View Solution→

QJEE MAIN 20262026

\text { Let } 0<\alpha<1, \beta=\frac{1}{3 \alpha} \text { and } \tan ^{-1}(1-\alpha)+\tan ^{-1}(1-\beta)=\frac{\pi}{4} \text {. Then } 6(\alpha+\beta) \text { is equal to: }

JEE MainMathematicsEasy

View Solution→

QJEE MAIN 20262026

If the distance of the point $(a, 2,5)$ from the image of the point $(1,2,7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is...

JEE MainMathematicsEasy

View Solution→