Work Energy and...

In a simple hydraulic press, the cross-sectional area of the two cylinders is $$5\times 10^{-4}m^2$$ and $$10^{-2}m^2$$, respectively. A force of $$20$$N is applied at the small plunger. How much work is done by the operator, if the smaller plunger moves down $$0.1$$m?

A vertical spring of force constant $$100$$N/m is attached with a hanging mass of $$10$$kg. Now an external force is applied on the mass so that the spring is stretched by additional $$2$$m. The work done by the force F is? $$(g=10 m/s^2)$$

A block is attached with a spring and is moving towards a fixed wall with speed V as shown in figure. As the spring reaches the wall, it starts compressing. the work done by the spring on the wall during the process of compression is

A ball moving with a velocity of 6 m/s strikes an identical stationary ball. After collision each ball moves at an angle of $$30^{\circ}$$ with the original line of motion. What are the speeds of the balls after the collision?

The diagram shows a barrel of weight $$1.0 \times 10^3$$ N on a frictionless slope inclined at $$30^0$$ to the horizontal. A force is applied to the barrel to move it up the slope at constant speed. The force is parallel to the slope. What s the work done in moving the barrel a distance of 5.0 m up the slope?

A practical of mass $$m$$ is moving in $$X-Y$$ plane under the action of a central force $$\overrightarrow { F }$$ in such a manner that at any instant $$t$$, the components of the velocity of the particle are-$${ v }_{ x }=4\cos { t,{ v }_{ y }=4sint} $$Then the amount of the work done by the force in a time interval $$t=0$$ to $$t$$ is-

A uniform rod AB of length land mass m is lying on a smooth table. A small particle of mass m strike the rod with a velocity $$V_{0}$$ at point C a distance X from the centre O. The particle comes to rest after collision. The value of x, so that point A of the rod remains stationary just after collision is:

The collision of two balls of equal mass takes place at the origin of co-ordinates. Before collision, the components of velocities are ($$y_{x}=50 cm/s$$, $$v_{v}=0)$$ and $$(v_{x}=-40 cm/s)$$ and velocity components ($$v_{x}$$ and $$v_{y}$$ respectively) of the second ball are: 

Two identical balls  are released from positions as shown. They collide elastically on horizontal surface. Ratio of heights attained by A & B after collision is( All surface  are smooth,neglect energy loss at M & N)

A car weighing 1 ton is moving twice as fast as another car weighing 2 ton. The kinetic energy of the one-ton car is