System of Parti...

Two pendulums each of mass $$m _ { 1 }$$ and $$m _ { 2 }$$ and length l are initially at rest as shown in figure. The ball of $$m _ { 1 } ,$$ is released and it strikes the ball of $$m _ { 2 } ,$$ if collision is perfectly inelastic, find the rise of centre of mass of the system after collision:

A ladder PQ of length 5m 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 M from the ground. Calculate the velocity of centre of mass of the rod at this moment.

A piece of paper is in the form of square . Two corners of these square are folded to make it appear like figure $$2$$ . Both the corners are put together at center of square $$O$$ . If $$O$$ is taken to be $$(0,0)$$ , the center of mass of new will be :

Distance of the center of mass of a solid uniform cone from its verted is zo. If the radius of its base isand its height is h, then zo is equal to 

linear mass density of a rod AB ( of length l) waries with distance X from end A of the rod as given by $$\lambda =\lambda _{0}x^{4}$$  Here $$\lambda _{0}$$  is constant.   Distance of centre of mass of the rod from end B is 

Two hail stones with radii in the ratio of 1 : 2 fall from a great height through the atomosphere. Then the ratio of their momenta after they have a attained terminal velocity is.

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is $$r$$ . Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become

Two bodies of masses 2 kg and 4 kg are moving with velocities 2 m/s and 1 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass ?

A thin rod of length 4l mass 4 m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O& perpendiular to the plane of the paper

The figure shows four objects rotating about an axis passing through CM. Which of these has angular momentum about the center of mass in direction of angular velocity