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Solve! - Gravitation - JEE Main

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)
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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

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