Work Energy and...

A particle moves along x-axis under the action of a position dependent  force $$ F= (5x^2-2x) N $$. work done by forces on the particle when it moves from origin to x=3 m is 

A particle of mass 2kg is moving in a circular path of radius 1m with a speed that varies with time as $$v=(t^2-t)m/s$$. The force acting on the particle at t=2s is

A block of mass m is connected rigidly with a smooth plank by a light spring of stiffness K. If the plank is moved with constant velocity $${ \upsilon  }_{ 0 }$$, find the work done by the external agent till the maximum compression of the spring.

A particle is moving in a force field given by F $$=$$ $${y^2}i - {x^2}j$$. starting from A, the particle has to reach C either along ABC or ADC. Let the work done along the two paths be $${W_1}$$ and $${W_2}$$ respectively. Then ($${W_1}$$,$${W_2}$$) are 

A heavy particle hanging from a fixed point by a light inextensible  string of length  l h projected horizontally with a speed of $$\sqrt { { g }^{ l } } $$. Find the speed of the particle and the inclination of the string to the vertical at the instant of the motion, when the tension in the string is equal to the weight of the particle.

The distance x moved by a body of mass 0.5 kg by a force varies with time as $$ x = 3t^2 + 4t + 5 $$, x is expressed in meter and t is seconds. The work done by force in first 2 seconds.

A strign of length $$1=1m$$ is fixed at one end and carries a mass of $$100gm$$ at other end. The string makes $$\sqrt { 5 } \pi$$ revolutions per second about a vertical axis passing through its second end. What is the angle of inclination of the string with the vertical?

A body of mass m is moved up the  plane of varying slope by a tangential force up to height h.The coefficient of friction between the surface and the block is $$\mu $$.
1.The work done on the block.

The displacement time graph of a uniformed accelerating body of mass 2 kg. initially at rest is shown below  the magnitude of force acting on the body is 

Two bodies A and B have masses $$20\ kg$$ and $$5\ kg$$ respectively . Each one is acted upon by a force of $$4\ kg.-wt$$. If they acquire the same kinetic energy in times $$t_{ A }\  and\ t_{ B }$$, then the ratio $$\dfrac { t_{ A } }{ t_{ B } } $$: