Work Energy and...

Two equal masses are attached to the two ends of a spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass during the above stretching is?

A simple pendulum with bob of mass $$m$$ and length $$x$$ is held in position at an angle $$1$$ and then angle $$2$$ with the vertical. When released from these positions, speeds with which it passes the lowest positions are $${v}_{1}$$ and $${v}_{2}$$ respectively. Then, $$\cfrac { { v }_{ 1 } }{ { v }_{ 2 } } $$ is 

The work done in joules in increasing the extension of a spring of stiffness $$10\ N/cm$$ from $$4\ cm$$ to $$6\ cm$$.

A block of mass $$M$$ at the end of the string is whirled round a vertical circle of radius $$R$$. The critical speed of the block at the top of the swing is

The mass of bucket full of water is 15 kg . It is being pulled up from a 15 m deep well. Due to a hole in the bucket 6 kg water flows out of the bucket at a uniform rate. The work done in drawing the bucket out of the well will be $$(g=10 m/s^2)-$$

If the force constant of a wire is $$K$$, the work done in increasing the length of the wire by/ is

A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity $$\sqrt{3gr}$$ at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is

A pendulum string of length $$l$$ is moved upto a horizontal position and released as shown in figure. If the mass of pendulum is $$m$$, then what is the minimum strength of the string that can withstand the tension as the pendulum passes through the position of equilibrium? 
(neglect mass of the string and air resistance)

The work done by external agent in stretching a spring of force constant $$k = 100\ N/cm$$ from deformation $$x_{1} = 10$$ to deformation $$x_{2} = 20\ cm$$.

A particle is projected so as to just move along a vertical circle of radius $$r$$ with the help of the massless string. The ratio of the tension in the string when the particle is at the lowest and highest point on the circle is?