QJEEM17Phf9e7: JEE Main 2017 Physics - Class 11 JEEM17Phf9e7 Solution: The mass density of a spherical body is given by ρ (r) = k r…

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QJEEM17Phf9e7: JEE Main 2017 Physics - Class 11 JEEM17Phf9e7 Solution: The mass density of a spherical body is given by ρ (r) = k r…

The mass density of a spherical body is given by

ρ

(r) =

\frac{k}{r}

for r

\leq

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 :

Multiple Choice Options

A https://ik.imagekit.io/novatra/photos/64a12f4d5abd2df28bfe1d16ef76087c3a65282686620cd430ca5d148bba3d50.webp
B https://ik.imagekit.io/novatra/photos/056ba8b993edb71e4c34a380f234dff95b431eb2e7060cfef1b43d39bd1d31fe.webp
C https://ik.imagekit.io/novatra/photos/ac57dbc996d93be950e8d9ae63f91d8323eaa330218d12423ee8b58747d3cd4c.webp
D https://ik.imagekit.io/novatra/photos/5e43504affd1e54786e37229ebf0dd6fb8753156b608f0094003a0b9b3d42271.webp

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Accepted Answer

For inside the spherical body, we have

$\frac{m}{v} = \frac{k}{r}$

$\Rightarrow m = \frac{k v}{r}$

Therefore, $g = \frac{G m r}{R^{3}} = \frac{G}{R^{3}} (\frac{k v}{r}) r$ = constant

For inside the spherical body, we have

$g_{o u t} = \frac{G M}{R^{2}}$

Therefore, the correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is the one depicted in option (c).

QJEEM17Phf9e7: JEE Main 2017 Physics - Class 11 JEEM17Phf9e7 Solution: The mass density of a spherical body is given by ρ (r) = k r…

Multiple Choice Options

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