Calculate The Change In The Values Of Energy And Angular Momentum When A Two Body System Interacting Through Gravitational Force Is Reduced To An Equivalent One Body Problem.

Change In Total Energy: Let us consider a two body system of masses and having position position vectors and respectively with respect to the origin O. The distance between and…

Continue ReadingCalculate The Change In The Values Of Energy And Angular Momentum When A Two Body System Interacting Through Gravitational Force Is Reduced To An Equivalent One Body Problem.

Consider The Motion Of Two Masses m1 and m2. Calculate The Kinetic Energy Of The Particles In The Centre Of Mass Frame Of Reference.

Ans. Fig. 1 Let us consider a system of two masses and having position vectors and respectively with respect to the origin O. If be the position vector of the…

Continue ReadingConsider The Motion Of Two Masses m1 and m2. Calculate The Kinetic Energy Of The Particles In The Centre Of Mass Frame Of Reference.

Two Particles Of Masses m1 And m2 Have A Relative Motion. Under What Condition Does Their Centre Of Mass Remains Stationary?

Ans. Let us consider two particles of masses and having position vectors and respectively with respect to the origin O, have a relative motion between them. Their centre of mass…

Continue ReadingTwo Particles Of Masses m1 And m2 Have A Relative Motion. Under What Condition Does Their Centre Of Mass Remains Stationary?

A Particle Is Moving In A Circular Orbit Of Radius “r” With A Speed “V”. Show That The Curl Of “V” is Equal To 2ω, Where ω Is The Angular Velocity Of The Particle. Also Show That The Angular Momentum Is Conserved.

Ans. Let us consider the position vector of the particle is given by, and the angular velocity of that particle is given by, Therefore, now and, Therefore, Again we know…

Continue ReadingA Particle Is Moving In A Circular Orbit Of Radius “r” With A Speed “V”. Show That The Curl Of “V” is Equal To 2ω, Where ω Is The Angular Velocity Of The Particle. Also Show That The Angular Momentum Is Conserved.

A Quadrilateral ABCD Has Masses 1,2,3 And 4 Units Located At Its Vertices A(-1,-2,2), B(3,2,-1), C(1,-2,4) And D(3,1,2). Find The Coordinate Of The Centre Of Mass.

Ans. Position vector of A is Position vector of B is Position vector of C is and Position vector of D is . So the centre of mass of the…

Continue ReadingA Quadrilateral ABCD Has Masses 1,2,3 And 4 Units Located At Its Vertices A(-1,-2,2), B(3,2,-1), C(1,-2,4) And D(3,1,2). Find The Coordinate Of The Centre Of Mass.

Two Particles Having Masses “m1” And “m2” Move So That Their Relative Velocity is “v” And The Velocity Of Their Centre Of Mass Is “V”. Calculate The Total Potential Energy.

Ans. Let us consider two particles of masses and having position vector and with respect to the origin O. Let be the position vector of centre of mass C with…

Continue ReadingTwo Particles Having Masses “m1” And “m2” Move So That Their Relative Velocity is “v” And The Velocity Of Their Centre Of Mass Is “V”. Calculate The Total Potential Energy.

Prove That The Total Momentum Of A System Is Constant i.e., Conserved Then The Centre Of Mass Is Either At Rest Or In Motion With Constant Velocity.

Ans. Let us consider be the position vector of ith particle of a system of n particles with respect to the origin and be the velocity of that ith particle…

Continue ReadingProve That The Total Momentum Of A System Is Constant i.e., Conserved Then The Centre Of Mass Is Either At Rest Or In Motion With Constant Velocity.

Prove That The Centre Of Mass Of A System Of Particles Moves As If The Total Mass And The Resultant External Force Were Applied At This Point.

Let us consider be the resultant external force acting on the ith particle of a system of n particles and be the internal force on the ith particle due to…

Continue ReadingProve That The Centre Of Mass Of A System Of Particles Moves As If The Total Mass And The Resultant External Force Were Applied At This Point.