Question

1. a) Derive a n expression for gravitational potential due to spherical shell at a point outside
the shell.
withoorem in gravitation​

Answer 1

Answer: The gravitational potential due to spherical shell at a point outside the shell is given by V = -GM/r , where M is mass of shell and r is distance between centre of shell and the point.

Explanation:

Mass of shell = M

Let the potential denoted by V and gravitational field be denoted by E.

Gravitational field and potential are related by the formula :

$E = \frac{-dV}{dr}$

$\int\ {E} \, dr = \int\ {-1} \, dV$

Gravitational field at a point outside the shell is given by $E = \frac{-GM}{r^{2} }$

∴ $\int\ {\frac{-GM}{r^{2} } } \, dr = \int\ {-1} \, dV$

$\frac{GM}{r} + c = -V$ ( c ⇒ constant of integration)

$V = \frac{-GM}{r} - c$

At infinity potential is assumed to be zero,

∴ as r → infinity , V → 0

∴ c = 0

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

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Answer 2

Answer:

The gravitational potential due to a spherical shell at a point outside the shell is given by the formula V = -GM/r, where M is the mass of the shell and r is the distance between the shell's centre and the point.

Explanation:

Shell mass equals M

Let the potential and gravitational fields be connected by the following formula:

E = -dV/dr

∫Edr = ∫-1dV

The gravitational field is determined with the help of equation E = -GM/r² for a point that is present outside the shell.

Therefore, ∫ -GM/r² dr = ∫ -1 dV

GM/r + c = - V

V = - GM/r - c

Let the potential be assumed as 0 in infinity.

Therefore, as r → infinity, V → 0

Therefore, c = 0

Therefore, V = -  GM/r

Thus, The gravitational potential due to a spherical shell at a point outside the shell is given by the formula V = -GM/r, where M is the mass of the shell and r is the distance between the shell's centre and the point.

#SPJ2