Work Energy and...

The bob $$A$$ of a pendulum of mass $$m$$ released from horizontal to the vertical hits another bob $$B$$ of the same mass at rest on a table as shown in figure. If the length of the pendulum is $$1\ m$$, what is the speed with which bob $$B$$ starts moving. (Neglect the size of the bobs and assume the collision to be elastic) (Take $$g = 10\ ms^{-2})$$.

A small block of mass m is pushed on a smooth track from position A with a velocity $$2\sqrt5$$ times the minimum velocity required to reach point D. The block will leave the contact with track at the point where normal force between them becomes zero.
When the block reaches point B, what is the direction (in terms of angle with horizontal) of acceleration of the block?

Two bodies $$A$$ and $$B$$ have masses $$20\ kg$$ and $$5\ kg$$ respectively. If they acquire the same kinetic energy. Find the ratio of thier velocities.

A spring lies along the x-axis attached to a wall at one end and a block at the other end. The block rests on a friction less surface at x = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement  $$x_{max}$$.
During the displacement, which of the curves shown in the graph best represents the work done on the spring block system by the applied force?

An elastic spring of unstretched length $$L$$  and force constant $$K$$, is stretched by a small length $$x$$. It is further stretched by another small length $$y$$. calculate the work done during the second stretching is:

 A string wraps around a fat pipe as a bob attached to the string is made to move in a circular path in the horizontal. Assuming the speed is somehow held constant as the radius diminishes due to the wrapping, how will the centripetal force change?
 

A body is acted upon by a force which is proportional to the distance covered. If distance covered is represented by s, then work done by the force will be proportional to.

Under the action of a force, $$2kg$$ body moves such that its position $$x$$ as a function of time is given by $$x={t}^{3}/3$$ where $$x$$ is in meters and $$t$$ in seconds. The work done by the force in the first two seconds is:

A uniform elastic string has length $$a_{1}$$ when tension is $$T_{1}$$ and length $$a_{2}$$ when tension is $$T_{2}$$. The amount of work done in stretching it from its natural length to a length $$(a_{1}+ a_{2})$$ is ?

The position $$x$$ of a particle moving along $$x-$$axis at time $$(t)$$ is given by the equation $$t=\sqrt x+2$$, where $$x$$ is in metres and $$t$$ in seconds. Find the work done by the force in first four seconds.