# Mechanics-II: Quick Revision of Formulae for IIT JEE, UPSEE & WBJEE

Find important formulae from unit Mechanics-II for quick revision. These formulae are very useful during competitive examination. This unit includes chapters – Centre of Mass, Rotational Motion and Gravitation.

When exams are round the corner then it is not possible to revise complete books so we have come up with unit wise formulae and important terms. Once you have gone through chapters thoroughly and understood it well there is no need to study it again and again. You can only revise important formulae and terms which will save your precious time.

In this regard find Electrostatics and Electric Current important Formulae for Quick Revision. These formulae will be helpful in various engineering entrance examinations such as IIT JEE, UPSEE, WBJEE etc.

In UPSEE and WBJEE where most of questions are asked directly on formulae, this quick revision note is very important.

**Mechanics-II**

**Two point system:**

where, *X* is distance of point *C* from *O*

**n-point system:**

** **

- The centre of mass of a system of particles moves as if all the mass of the system was concentrated at the centre of mass and all the external forces were applied at that point.

- The total momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its centre of mass.

- Collision are classified in two categories: Elastic Collision and Inelastic Collision

- In an elastic collision kinetic energy and momentum both are conserved.

- In an inelastic collision kinetic energy is not conserved while momentum is still conserved.

- When two colliding objects stick together and move together with a common velocity then collision is referred to as completely inelastic.

- When a large force acts for a short interval of time, then product of force and time is called impulse. It is a vector quantity denoted by j.

- A thrust force will act when mass of a system either increases or decreases.

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- The angle of rotation is measured in radians.

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- Parallel axis theorem relates moment of inertia through center of mass to moment of inertia with respect to some other axis

Mathematically, I = I_{cm} + Md^{2}

- If x and y are two perpendicular axis lying in the plane of the body and z is the axis perpendicular to the plane of the body and passing through point of intersection of x and y, then I
_{z}= I_{x}+ I_{y }

**Law of orbits:**All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse**Law of areas:**The line that joins any planet to the sun sweeps equal areas in equal intervals of time .**Law of periods:**The square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet.- Gravitational force between two point masses is

- Acceleration due to gravity on the surface of the earth is

- The value of acceleration due to gravity vary due to the following factors:

(a) Shape of the earth

(b) Height above the earth surface

(c) Depth below the earth surface

(d) Axial rotation of the earth.

- Acceleration due to gravity at height
*h*from the surface of the earth is

- Acceleration due to gravity at depth
*d*from the surface of the earth

- Variation in
*g*due to rotation of earth at latitude Φ

- Gravitational potential difference is defined as the work done to move a unit mass from one point to the other in the gravitational field. The gravitational potential difference in bringing unit test mass
*m*from point*A*to point*B*under the gravitational influence of source mass*M*is

- The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force.

where U, = Gravitational potential energy

- The minimum velocity with which a body must be projected up so as to enable it to just overcome the gravitational pull, is known as escape velocity.

- Time period of satellite is the time taken by satellite to go once around the earth.

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