Gravitational Field & Potential — Shell theorem
Gravitation
10
JEE Qs
8%
Hard
75
min
Master the graphs of gravitational field and potential versus distance for both spherical shells and solid spheres, as they are frequently tested.
🧮 Key Formulas
✅ Key Points for JEE
- 1For a uniform spherical shell, the gravitational field at any point *outside* the shell is the same as if all its mass were concentrated at its center.
- 2The gravitational field intensity at any point *inside* a uniform spherical shell is zero.
- 3The gravitational potential at any point *inside* a uniform spherical shell is constant and equal to the potential on its surface.
- 4Gravitational field (E) is discontinuous at the surface of the shell, while gravitational potential (V) is continuous at the surface.
- 5Graphs of E vs r and V vs r are crucial; E changes abruptly at R from 0 to GM/R^2, then decreases as 1/r^2. V is constant inside, then decreases as -1/r outside.
⚠️ Common Mistakes
- ✕Confusing the gravitational field (E=0) and potential (V=constant) inside a spherical shell.
- ✕Applying the shell theorem results for a *shell* directly to a *solid sphere* without understanding the superposition principle or the separate derivation for a solid sphere.
- ✕Incorrectly assigning negative signs for potential or directions for the field, especially when dealing with vector components.
- ✕Misinterpreting 'r' as the radius of the shell instead of the distance from the center to the point of interest.
📝 Practice Questions
See allQ38.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R): The mass 2025 (22 Jan Shift 2) JEE Main Previous Year Paper of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below : (1) (A) is false but (R) is true (2) (A) is true but (R) is false (3) Both (A) and (R) are true and (R) is the correct (4) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A)
Q42.A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that θ(t) = 5t2 −8t, where θ(t) is the angular position of the rotating disc as a function of time t. How much power is delivered by the applied torque, when t = 2 s ? (1) 72MR2 (2) 8MR2 (3) 108MR2 (4) 60MR2
Q37.Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be : (1) 2.8 (2) 11.2 (3) 5.6 (4) 8.4 → sin [ω (t −zc )] (S.I. Units). The
Q35.A small point of mass m is placed at a distance 2R from the centre ' O′ of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is F1 . A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F2 . The value of ratio F1 : F2 is (1) 12 : 11 (2) 11 : 10 (3) 12 : 9 (4) 16 : 9
Q41.If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected. (1) 27 days (2) 1 day (3) 81 days (4) 3 days
Q49.A satellite of mass M is revolving around earth in a circular orbit at a height of R from earth surface. The 2 3 angular momentum of the satellite is . The value of x is ______ , where M and R are the mass and M√GMRx radius of earth, respectively. ( G is the gravitational constant)
NCERT Chapters
- Class 11 Physics Ch 8: Gravitation