** GRAVITATION **

Subtopic1. The Action of Forces and Torques on Rigid Objects, 2. Rigid Objects in Equilibrium, 3. Center of Gravity, 4. Newton’s Second Law for Rotational Motion about a Fixed Axis, 5. Rotational Work and Energy, 6. Angular Momentum, 7. Concepts & Calculations.

With solution Model exam and free Mock test papers in pdf format for JEE-Mains entrance exams taker. Mostly questions are solved and few unsolved question paper to test your knowledge are also included. JEE Mains MCQ (Multiple Choice Question) from Physics, Chemistry and Mathematics.

**JEE Mains MCQ Problems / Practice Sample Papers on Gravitation with Solutions free pdf.**

01. Gravitation JEE Mains MCQ Pattern Sample / Question Papers (Download herePDF.)

JEE Main Question Paper Solution on Gravitation (Download herePDF.)

01. Problems of Gravitation on JEE Mains MCQ Pattern (Download herePDF.)

Gravitation Question Paper Solution on JEE Main level(Download herePDF.)

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**KEPLER’S LAW FOR SATELLITES, ORBITAL SPEED AND ESCAPE SPEED**

Question

A satellite is established in a circular orbit of radius r and another in a circular orbit of radius 1.01 r. How much percentage the time period of second-satellite will be larger than the first satellite nearly.

**UNIVERSAL LAW OF GRAVITATION**

Question

The typical adult human brain has a mass of about 1.4 kg. What force does a full moon exert on such a brain when it is directly above with its centre 378000 km away ? (Mass of the moon = 7.34 × 10^{22} kg)

Question

Solid spheres of same material and same radius ‘r’ are touching each other. If the density is ‘ρ’ then find out gravitational force between them.

**Some Practice Example of Gravitation**

**Example : 1**

A satellite is launched into a circular orbit 1600 km above the surface of the earth. Find the period of revolution if the radius of the earth is R = 6400 km and the acceleration due to gravity is 9.8 m/sec^{2}. At what height from the ground should it be launched so that it may appear stationary over a point on the earth’s equator?

**Example : 2**

Find potential at a point ‘P’ at a distance ‘x’ away from centre of a uniform ring of mass M and radius R.

**Example : 3**

Calculate the velocity with which a body must be thrown vertically upward from the surface of the earth so that it may reach a height of 10 R, where R is the radius of the earth and is equal to 6.4 × 10^{8} m. (Earth’s mass = 6 × 10^{24} kg,

Gravitational constant G = 6.7 × 10^{–11} nt-m^{2}/kg^{2})

**Example : 4**

In a double star, two stars (one of mass m and the other of 2m) distant d apart rotate about their common centre of mass. Deduce an expression of the period of revolution. Show that the ratio of their angular momenta about the centre of mass is the same as the ratio of their kinetic energies.

**Problem : 5**

For a particle projected in a transverse direction from a height h above Earth’s surface, find the minimum initial velocity so that it just grazes the surface of earth path of this particle would be an ellipse with center of earth as the farther focus, point of projection as the apojee and a diametrically opposite point on earth’s surface as perigee.

**Some Gravitation Practice Problems**

**Problem : 1**

The centres of two identical spheres are at a distance 1.0 m apart. If the gravitational force between them is 1.0 N, then find the mass of each sphere. (G = 6.67 × 10^{–11} m^{3} kg^{–1} sec^{–1})

**Problem : 2**

Three identical bodies of mass M are located at the vertices of an equilateral triangle with side L. At what speed must they move if they all revolve under the influence of one another’s gravity in a circular orbit circumscribing the triangle while still preserving the equilateral triangle ?

**Problem : 3**

Find the distance of a point from the earth’s centre where the resultant gravitational field due to the earth and the moon is zero. The mass of the earth is 6.0 × 10^{24} kg and that of the moon is 7.4 × 10^{22} kg. The distance between the earth and the moon is 4.0 × 10^{5} km.

**Problem : 4**

Calculate gravitational field due to a uniform ring of mass M and radius R at a distance x from center of ring.

**Problem : 5**

Calculate gravitational field at a distance x from centre of a uniform disc of mass M and radius R.

**GRAVITATIONAL POTENTIAL ENERGY**

Gravitational potential energy of two mass system is equal to the work done by an external agent in assembling them, while their initial separation was infinity. Consider a body of mass m placed at a distance r from another body of mass M.

**KEPLER’S LAW FOR PLANETARY MOTION**

Suppose a planet is revolving around the sun, or a satelite is revolving around the earth, then the planetary motion can be studied with help of Kepler’s three laws.

**Law of areal velocity :**

To understand this law, lets understand the angular momentum consarvation for the planet. If a planet moves in an elliptical orbit, the gravitation force acting on it always passes through the centre of the sun. So torque of this gravitation force about the centre of the sun will be zero. Hence we can say that angular momentum of the planet about the centre of the sun will remain conserved (constant)

τ about the sun = 0

**CIRCULAR MOTION OF A SATELLITE AROUND A PLANET**

Suppose at satellite of mass m_{0} is at a distance r from a planet. If the satellite does not revolve, then due to the gravitational attraction, it may collide to the planet. To avoid the collision, the satellite revolve around the planet, for circular motion of satellite.

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**Entrance Exams Preparation Tips**

*(a) Revise and re-revise. At least 3-4 revisions are a must before you start taking mock tests.*

*(b) Buy objective books and practice answering questions. Attempt questions one by one and when you are finished, correct your responses.*

*(c) Test yourself on individual topics. Once you feel you are doing well in a given topic, obtain a sample test for the subject. *

*(d) Take mock tests (of the same three and a half hour length) one month prior to the test.*

*(e) Evaluate how many questions you marked incorrectly. Identify problem topics and revise before proceeding to the next chapter or next section.*

*(f) Do not study the day before the test. What you have studied until then is enough. *

*(g) Many candidates use coaching centers or private tutors to prepare. You may choose to do so, but before choosing one, identify your needs.*

*(h) Do not buy too many books. It’s better to read one book 10 times than read 10 books one time.*

*(i) Sample test questions will give you a feel for what the test looks like. Make sure to go through these before test day.*

*(j) Stop reading new fundamentals just before the exam. One month before the exam, concentrate on taking mock tests and revise what you have studied.*

*(k) Have a light snack before leaving for the examination center. This is a must to keep you energized during exam. Keep a water bottle with you during the exam, this will not only help with thirst, but help you to maintain a cool temperament during the examination.*

*(l) Reach your examination center at least 30-40 minutes in advance to avoid any last minute hassle.*

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