Question

A particle of mass M is placed at the centre of a uniform spherical shell of equal mass and radius a. Find the gravitational potential at a point P at a distance a/2 from the centre.

Answer 1

•A PARTICLE OF MASS M IS PLACED AT THE CENTRE OF A UNIFORM SPHERICAL SHELL OF EQUAL MASS AND RADIUS 'a'. THEN THE GRAVITATIONAL POTENTIAL AT A POINT P AT A DISTANCE a/2 FROM THE CENTRE WILL BE 3GM/a.

• To find the GRAVITATIONAL POTENTIAL AT A POINT AT DISTANCE a/2 FROM THE CENTRE, We must use the formula

Vp= Vsphere + Vparticle.

= GM/a + GM/(a/2)

= 3GM/a

Answer 2

Given:-

Radius = a

Mass = M

To Find:-

The Gravitational Potential at a distance of a/2.

Solution:-

Let V be the gravitational potential

Gravitational potential at a distance $\frac{a}{2}$ will be V₁ = $\frac{-GM}{\frac{a}{2} }$ = $\frac{-2GM}{a}$.......(1)

And gravitational potential at a distance a will be V₂ = $\frac{-GM}{a}$..................(2)

Therefore the Net Gravitational Potential

   Vp = V₁ + V₂

Vp =  $\frac{(-2GM)}{a}$ + $\frac{(-GM)}{a}$

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

Magnitude of Gravitational Potential Vp = $\frac{3GM}{a}$