Work Energy and...

A spring of force constant k is cut in two parts at its one-third length. When both the parts are stretched by same amount. The work done in the two parts will be:
(Note- Spring constant of a spring is inversely proportional to length of spring.)

A pendulum bob is raised to a height, $$h$$, and released from rest. At what height will it attain half of its maximum speed?

A simple pendulum of length $$l$$ has maximum angular displacement $$\displaystyle \theta .$$ Then maximum kinetic energy of a bob of mass $$m$$ is

A particle of mass $$m$$ moves on a straight line with its velocity varying with the distance travelled according to the equation $$\displaystyle v= \alpha \sqrt{x},$$ where a is a constant. Find the total work done by all the forces during a displacement from $$x=0$$ to $$x=d$$.

The kinetic energy of particle at the lower most position is

A block of mass $$m=2$$ kg is pulled by a force $$F=40$$ N upwards through a height $$h=2 m$$. Find the work done on the block by the applied force F and its weight mg. $$\displaystyle \left ( g= 10 m/s^{2} \right )$$

A force $$F$$ acting on a particle varies with the position $$x$$ as shown in figure. Find the work done by this force in displacing the particle from $$\displaystyle x= 0\ m\:to\:x= 2\  m.$$

A block is constrained to move along x-axis under a force F=-2x. Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=2 m to x=-4 m.

A force $$F=(2+x)$$ acts on a particle in x-direction where $$F$$ is in newton and $$x$$ in meter. Find the work done by this force during a displacement from $$x=1.0$$ m to $$x=2.0\ m$$.

A block is constrained to move along x-axis under a force $$\displaystyle F= \frac{4}{x^{2}}\left ( x\neq 0 \right ).$$ Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=4 m to x=2 m.