You visited us 1 times! Enjoying our articles? Unlock Full Access!

Gravitational Potential of a Solid Sphere

A solid spher...

Question

A solid sphere of mass $2 M$ and radius $R$ is enclosed by a spherical shell of mass $M$ and radius $2 R$ . Then, the potential at a point $P$ on the surface of the solid sphere is:

\frac{- G M}{R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 4 G M}{R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 5 G M}{R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 5 G M}{2 R}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{- 5 G M}{2 R}$

Potential due to solid sphere, at its surface is given by

$V_{1} = \frac{- G (2 M)}{R}$

Potential due to spherical shell is given by,

At the point $P$ , $V_{2} = \frac{- G M}{2 R}$

Total potential at point $P$ ,

$V_{n e t} = V_{1} + V_{2}$

$V_{n e t} = \frac{- G (2 M)}{R} + \frac{- G M}{2 R}$

$V_{n e t} = \frac{- 5 G M}{2 R}$

Hence, option $(D)$ is the correct answer.

Suggest Corrections

Similar questions

Q. A spherical shell of mass

M / 2

is enclosing a solid sphere of mass

3 M

and radius

2 R

. Then ratio of potential because of the spherical shell and the solid sphere at their common centre is

Q. A uniform solid sphere of mass M and radius R is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2R. The value of gravitational potential at a distance

\frac{3}{2} R

from the centgre is :-

Q. A uniform solid sphere of mass

m

and radius

r

is surrounded symmetrically by a uniform thin spherical shell of radius

2 r

and mass

m

. Choose the correct statement

A solid metallic sphere of radius r is charged to a voltage V. It is enclosed by a thin spherical shell of radius 2r. If q is the charge on the sphere and the shell each, the potential difference between them will be $\frac{x V}{2}$ . What is x? ___

Q. A uniform solid sphere of mass

M

and radius

R

is surrounded symmetrically by a uniform thin spherical shell of mass

\frac{M}{2}

and radius

2 R

. Then gravitational field at a distance of

\frac{5}{2} R

from the centre is

Join BYJU'S Learning Program

A solid sphere of mass 2M and radius R is enclosed by a spherical shell of mass M and radius 2R. Then, the potential at a point P on the surface of the solid sphere is:

The correct option is D −5GM2R Potential due to solid sphere, at its surface is given by V1=−G(2M)R Potential due to spherical shell is given by, At the point P ,V2=−GM2R Total potential at point P, Vnet=V1+V2 Vnet=−G(2M)R+−GM2R Vnet=−5GM2R Hence, option (D) is the correct answer.

A solid sphere of mass $2 M$ and radius $R$ is enclosed by a spherical shell of mass $M$ and radius $2 R$ . Then, the potential at a point $P$ on the surface of the solid sphere is: