What is centre of mass? Show that centre of mass of a system of particles is defined as the point whose position vec is given by `vecR = frac(Sigmam_1vecr_)(M)`

What is the position vector of centre of mass of two particles of equal masses?

Show that the total linear 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.

Two particles, each of mass m and speed v_3 travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is: (i)T,(II) T-(mv^2)//l, (iii) T+(MV^2)/l, (iv)0

Define the co-efficient of restitution. A particle of a mass m moving with a velocity u struck head-on against another particle of mass Km at rest.After collision the particles move with velocities V1 and V2 respectively.If the collision is prefectly elastic.Prove that the loss of kinetic energyof the particle with mass m is maximum when k=1.

A partical of mass m1 is travelling with avelocity u1 strikes head-on against partical of mass m2 at rest.After collision the particales move with a velocity v1 and v2 respectively .show that the ratio of decrese in K.E of the partical of mass m1 to its original K.E is given By (4m1m2)/(m1+m2)^2

Find the potential energy of a system of four particles each of mass m place at the vertices of a square fo side l. Also obtain the potential at the centre of the square.

A point particle of mass 0.1kg is excecuting SHM of amplitude 0.1m. When the particle passes through the mean position, its kinetic energy is 8xx10^(-3) J. Obtain the equation of motion of the particle if the initial phase’of oscillation is 45^@ .

Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s^2 . What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.)

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.