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P(r) is magnitude of physical quantity as a function of r (distance from centre of spherical distribution of radius R). Match the following columns and select the correct option from the codes given below.
Column-I Column-II
i.
p. P(r) is variation of gravitational potential for a uniform volumetric spherical distribution of
mass.
ii.
q. P(r) is variation of gravitational potential for a uniform spherical shell.
iii.
r. P(r is variation of gravitational field intensity for a uniform volumetric spherical distribution of mass.
iv.
s. P(r is variation of gravitational field intensity for a uniform spherical shell.
Codes:

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i-q, ii-s, iii-r, iv-p

i-q, ii-r, iii-s, iv-p

i-r, ii-s, iii-p, iv-p

i-s, ii-r, iii-q, iv-p

answer is C.

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Detailed Solution

Potential sphere $V = - \frac{GM}{2 R^{3}} (3 R^{2} - r^{2}) for r \leq R$

$V = - \frac{GM}{r} for r > R$

Shell $V = - \frac{GM}{r} for r \leq R$

$V = - \frac{GM}{r} for r > R$

Field sphere $E_{g} = \frac{GM}{R^{3}} . r for r \leq R$

$E_{g} = \frac{GM}{r^{2}} for r > R$

$Shell E_{g} = zero for r < R$

$E_{g} = \frac{GM}{r^{2}} for r \geq R$

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