System of Parti...

Which of the following is not correct about centre of mass ?

Four identical rods each of mass $$M$$ are joined to form as square frame. The moment of inertia of the system about an axis passing through the point of intersection of diagonals and perpendicular to the plane of the square is 

A man stands at one end of the open truck which can run on frictionless horizontal rails. Initially, the man and the truck are at rest. Man now walks to the other end and stops. Then which of the following is true?

For a rigid body made up of N particles each of mass m, the radius of gyration, about a given axis of rotation, equals to the

In situation (i), just after both A and B jump from the platform, velocity of centre of mass of the system (A, B and the platform) is :

Two particles A and B initially at rest, move towards each other by mutual force of attraction. At the instant when the speed of A is n and the speed of B is 3n, the speed of the centre of mass of the system is :

A particle having mass $$0.5\ kg$$ is projected under gravity with a speed of $$98\  m/sec$$ at an angle of $$60^{\circ} $$.The magnitude of the change in momentum $$($$in N sec$$)$$ of particle after  $$10\  seconds$$ is :

A uniform disc of mass $$M$$ and radius $$R$$ is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull $$T$$ is exerted on the cord, the tangential acceleration of a point on the rim is 

Two bodies of different masses of $$2 kg$$ and $$4 kg$$ are moving with velocities with $$2 {m}/{s}$$ and $$10  {m}/{s}$$ towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass?

For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of body?