Newton's Law of Gravitation — Force between masses
Gravitation
10
JEE Qs
8%
Hard
60
min
Master vector addition for finding the net force from multiple masses and always correctly identify 'r' as the distance between the centers of the interacting bodies.
🧮 Key Formulas
✅ Key Points for JEE
- 1Gravitational force is always attractive, acts along the line joining the centers of the two masses, and forms an action-reaction pair.
- 2It is a central and conservative force, independent of the medium between the masses.
- 3For extended, spherically symmetric bodies, 'r' is the distance between their geometric centers. For point masses, 'r' is the distance between them.
- 4The Principle of Superposition applies: the net gravitational force on a mass due to multiple masses is the vector sum of individual forces.
- 5Do not confuse the universal gravitational constant 'G' (a fixed scalar value) with 'g' (acceleration due to gravity, which is a vector and varies).
⚠️ Common Mistakes
- ✕Using 'r' as the radius of a mass or the distance between surfaces instead of the distance between the centers of masses/points.
- ✕Incorrectly performing vector addition when calculating the net force due to multiple masses (e.g., adding magnitudes instead of vectors).
- ✕Confusing the units and numerical values of 'G' (Universal Gravitational Constant) and 'g' (acceleration due to gravity).
📝 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