Home
Class 11
PHYSICS
A uniform solid sphere of mass M and rad...

A uniform solid sphere of mass M and radius a is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2a.Find the gravitational field at a distance a. `3/2 a` from the center

Text Solution

Verified by Experts



ure shows the situation. Thepoint `P_1` is at a distance `3/2a` from the cenre and `P_2 is at a distance `5/2a` from the centre. As `P_1` in inside the cavity of the thin spherical shell, the field here due to the shell is zero. the field due to the solid sphere is
`E=(GM)/((3/2a)^2)=(4GM)/(9a^2)`
This is also the resultant field. The direction is twoards the centre. the point `P_2` is outside the sphere as well as teh shell. Both may be replaced by single particles of the same mass at the centre.The field due to eac of them is
`E'=(GM)/((5/2a)^2)=(4GM)/(25a^2)`
The resultasnt field is E=2F=(8GM)/(25a^2)` towards the centre.
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    HC VERMA|Exercise Question for short Answers|19 Videos

  • GRAVITATION

    HC VERMA|Exercise Objective -1|17 Videos

  • GRAVITATION

    HC VERMA|Exercise Exercises|39 Videos

  • FRICTION

    HC VERMA|Exercise Exercises|31 Videos

  • HEAT AND TEMPERATURE

    HC VERMA|Exercise Exercise|34 Videos

Similar Questions

Explore conceptually related problems

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 (a)/(2) distance from the centre will be:

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The center of the ring is at a distance sqrt3 a from the center of the sphere. Find the gravitational force exerted by the sphere on the ring.

A uniform metal sphere of radius R and mass m is surrounded by a thin uniform spherical shell of same mass and radius 4R . The centre of the shell C falls on the surface of the inner sphere. Find the gravitational fields at points A and B .

a solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m is placed on the line joining the two centers as a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if a). rltxlt2r , b). 2rltxlt2R and c). xgt2R .

The radius of gyration of a uniform disc about a line perpendicular to the disc equals to its radius. Find the distance of the line from the centre.

Write down the moment of inertia of a disc of radius R and mass m about an axis in its plane at a distance R/2 from its centre.

A particle of mass 10g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to done against the gravitational force between them to take the particle is away from the sphere.

Find the moment of inertia of a uniform ring of mass M and radius R about a diameter.

The moment of inertia of a uniform semi-circular wire of mass 'M' and radius 'r' about a line perpendicular to the plane of the wire through the center is