# A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at $\frac{a}{2}$ distance frim the centre, will be: Option 1) $\frac {-3GM}{a}$ Option 2) $\frac{-2GM}{a}$ Option 3) $\frac{-GM}{a}$ Option 4) $\frac{-4GM}{a}$

D Divya Saini

As we learnt

Potential due to Uniform Ring -

$r=$ distance from ring

$a\rightarrow$ radius of Ring

$V\rightarrow$ Potential

- wherein

At a point on its Axis

$V=-\frac{GM}{\sqrt{a^{2}+r^{2}}}$

At the centre

$V=-\frac{GM}{a}$

$V_{p}=N_{spenual shell}+N_{particle}$

$\frac{Gm}{a}+\frac{Gm}{\frac{a}{2}}=\frac{3Gm}{a}$

Option 1)

$\frac {-3GM}{a}$

Correct Optino

Option 2)

$\frac{-2GM}{a}$

Incorrect Option

Option 3)

$\frac{-GM}{a}$

Incorrect Option

Option 4)

$\frac{-4GM}{a}$

Incorrect Option

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