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Question

A particle of mass M is situated at the centre of a spherial shell of same mass and radius R. The gravitational potential at a point situated at $${R}{2}$$ distance from the centre will be


A
3GMR
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B
2GMR
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C
GMR
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D
4GMR
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Solution

The correct option is A $$-\dfrac{3GM}{R}$$
Here, mass of the particle=M, Mass of the spherical shell=M, Radius of the spherical shell= R. Let O be centre of spherical shell. Gravitational potential at point P diue to particle at O is $${V}_{1}=\dfrac{GM}{\left(R/2\right)}$$

Gravitational potential at point P due to spherical shell is $${V}_{2}=\frac{GM}{R}$$

Hence, total gravitational potential at point P is $$V={V}_{1}+{V}_{2}$$

$$=-\dfrac{GM}{\left(R/2\right)}+\left(-\dfrac{GM}{R}\right)=-\dfrac{2GM}{R}-\dfrac{GM}{R}=-\dfrac{3GM}{R}$$

Physics

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