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.

Prove That The Total External Torque Acting On A System Of Particles Is Equal To The Time Rate Of Angular Momentum Of The System, Provided That The Internal Forces Between The Particles Are Central Forces (i.e., The Internal Forces Between Any Two Particles Are Always Directed Along The Line Joining The Particles).

Relation between angular momentum and total external torque: Let us consider be the resultant external force acting on the ith particle of a system of n particles and be the…

Continue ReadingProve That The Total External Torque Acting On A System Of Particles Is Equal To The Time Rate Of Angular Momentum Of The System, Provided That The Internal Forces Between The Particles Are Central Forces (i.e., The Internal Forces Between Any Two Particles Are Always Directed Along The Line Joining The Particles).