System of Parti...

A ladder $$PQ$$ of length $$5 m$$ inclined to a vertical wall is slipping over a horizontal surface with a velocity of $$2 ms^{-1}$$, when $$Q$$ is at a distance $$3 cm$$ from the ground. Calculate the velocity of centre of mass of the rod at this moment.

Two thin rods of mass $$m$$ and length $$l$$, each are joined to form a $$L$$ shape as shown. The moment of inertia of rods about an axis passing through free end (O) of a rod and perpendicular to both the rods is:

If two particles of masses $$m_1$$ and $$m_2$$ move with velocities $$v_1$$ and $$v_2$$ towards each other on a smooth horizontal plane, what is the velocity of their centre of mass. ?

A uniform rod AB of length l and mass m is free to rotate about A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is $$\dfrac{ml^2}{3}$$, the initial angular acceleration of the rod will be?

A sphere $$(C.O.M)$$ is moving at $$v_{0}$$ has angular velocity $$\dfrac {3v_{0}}{4\ R}$$ as show. Now  it placed on a rough horizontal surface. Its final velocity (of $$C.O.M$$) is:

A body is dropped from a height h, if it acquires a momentum p, then the mass of the body is:

A small block of mass $$m$$ is moving on a horizontal table surface at initial speed $$v_0$$. It then moves smoothly onto a sloped wedge of mass $$M$$ . The wedge can also move on the table surface. Assume that everything moves without friction. Which of the following statement(s) is (are) correct :-

The centre of mass of  non uniform rod of length $$L$$ whose mass per unit length $$\lambda$$ varies as $$\lambda=k{x}^{2}$$ where $$k$$ is a constant and $$x$$ is the distance of any point on rod from left end $$A$$ is (from the same end)

A thin rod of length $$4l$$, mass $$4$$m is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing through $$O$$ and perpendicular to the plane of the paper?

A light rod of length $$l$$ has two masses $$m_1$$ and  $$m_2$$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is