Displacement OF Centre OF Mass

Centre Of Mass|OMR

A particle of mass 1 kg has velocity vec(v)_(1) = (2t)hat(i) and another particle of mass 2 kg has velocity vec(v)_(2) = (t^(2))hat(j) {:(,"Column I",,"Column II",),((A),"Netforce on centre of mass at 2 s",(p),(20)/(9) unit,),((B),"Velocity of centre of mass at 2 s",(q),sqrt68 " unit",),((C ),"Displacement of centre of mass in 2s",(r ),(sqrt80)/(3) "unit",),(,,(s),"None",):}

Motion OF Centre OF Mass

Two boys A and B of masses 60kg and 40kg respectively are at the ends of a 4m long boat of mass 100kg which is on water in lake and the system is at rest.If the boys meet at the centre of the boat then find the displacement of centre of mass of the boat in meter (neglect friction between water and boat)

A light inextensible string, passing over a pulley, supports two particles 1 and 2 at its ends. An insect of mass m is sitting on particle 2 and the system is in equilibrium. The sum of masses of particles and the insect is M. Now the insect crawls a distance x up relative to the string. Find the displacement of centre of mass of the system of two particles and the insect. In which direction does the centre of mass move and why ?

According to the principle of conservation of linear momentum if the external force acting on the system is zero, the linear momentum of the system will remain conserved. It means if the centre of mass of a system is initially at rest, it will remain at rest in the absence of external force, that is, the displacement of centre of mass will be zero. A plank of mass M is placed on a smooth horizontal surface. light identical springs, each of stiffness K , are rigidly connected to struts at the end of the plank as shown in Fig. When the springs are in their unextended position, the distance between their free ends is 3l . A block of mass m is placed on the plank and pressed against one of the springs so that it is compressed to l . To keep the block at rest it is connected to the strut means of a light string. Initially, the system is at rest, Now the string is burnt. The maximum displacement of the plank is

Properties OF Centre OF Mass