Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

The mass density of a spherical body is given by ρ (r)= $\frac{k}{r}$ for r ≤ R and ρ (r)=0 for r > R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is

Option 1)

Option 2)

Option 3)

Option 4)

Answers (1)

best_answer

As we learnt in

Gravitational field Intensity -

$\vec{I}=\frac{\vec{F}}{m}$

$\vec{I}\rightarrow G.field\: Intensity$

$m\rightarrow mass\: of\: object$

$\vec{f}\rightarrow Gravitational\: Force$

- wherein

$Unit : \frac{Newton}{kg}\: or\: \frac{m}{s^{2}}$

$Dimension : \left [ M^{0}LT^{-2} \right ]$

Given that $p=\frac{m}{v}$ of spherical body $P(r)= \frac{k}{r}$

$\frac{m}{v} = \frac{k}{r} \: for\:inside\:r\leqslant R$

$m = \frac{kv}{r} .................(1)$

inside the surface of sphere intensity

$I= \frac{{Gm}r}{R^3}$ $\because I= \frac{F}{m}$

$g_{inside}= \frac{Gm}R^3{r}$ or $I= \frac{mg}{m}\:=g$

$= \frac{G}{R^3}\frac{kv}r{r}=\ \, \, \, constant\ from\ equation\:(1)$

$g_{out}=\frac{Gm}{r^2}$

Option 1)

Incorrect

Option 2)

Correct

Option 3)

Incorrect

Option 4)

Incorrect

Posted by

prateek

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 session 2 result date announced; Steps to check NTA session 2 scores

anam-khan

JEE Main 2024 session 2 final answer key soon at jeemain.nta.ac.in; result on April 25

anam-khan

JEE Main 2024 Session 2: Last day to challenge answer key today

Latest Question