System of Parti...

Two blocks of masses $$8$$kg are connected by a spring of negligible mass and placed on a frictions less horizontal surface. An impulse gives a velocity of $$12$$m/s to the heavier block in the direction of lighter block. The velocity of the center of mass is:-

Two particles having mass ratio n : 1 are interconnected by a light in extensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is

A thin uniform rod of length l and m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $$\omega$$. Its centre of mass rises to a maximum height of:

Linear mass density of a rod AB ( of length 10 m) varies with distance x from its end A as $$\lambda  = {\lambda _o}{x^3}$$$$\left( {{\lambda _o}\;{\text{is}}\;{\text{positive}}\;{\text{constant}}} \right)$$. Distance of the center of mass of the rod, from end B is

If the moment of inertia of a rigid body is numerically equal to its mass, its radius of gyration is  

In rotational motion of a rigid body, all particle move with

A man spinning in free space changes the shape of his body e.g. by stretching his arms or curling up then, which of the following physical quantity will remain constant

The moment of inertia of a uniform cylinder of length $$l$$ and radius $$R$$ about its perpendicular bisector is $$1$$. What is the ratio $$l/R$$ such that the moment of inertia is minimum?

Find the coordination of center of mass of a uniform semicircle closed wire frame with respect to the origin which is at its center.The radius of the circular portion is R.                

Six identical particles each of mass $$m$$ are arranged at the corners of a regular hexagon of side length $$a$$. If the mass of one of the particle is doubled, the shift in the centre of mass is