In the figure, pendulum bob on left side is pulled a side to a height $$h$$ from its initial position. After it is released it collides with the right pendulum bob at rest, which is of same mass. After the collision, the two bobs stick together and rise to a height

In the diagram shown below, $$m_1$$ and $$m_2$$ are the masses of two particles and $$x_1$$ and $$x_2$$ are their respective distances from the origin $$O$$.

The centre of mass of the system is

A neutron makes a head on elastic collision with a lead nucleus. The ratio of nuclear mass to neutron mass is 206 . The fractional change in kinetic energy of a neutron is

A bullet of mass $m$ hits a mass $$M$$ and gets embedded in it. If the block rises to a height $$h$$ as a result of this collision, the velocity of the bullet before collision is