Work

An object of mass m moves on a circular track of radius R with constant speed U. The work done by centripetal force after it completes one circle is 

Force acting on a particle is $F=3i-2j+4k$ and its displacement is given by $AB=(2,-1,0)$, then the work done is _____.

A force acting on a particle of mass$1\mathrm{kg}$ such that position of particle (x) is varying with time (t) as $\mathrm{x}=2{\mathrm{t}}^2-1$ where x is in m and t is in s. Work done by the force during $0 \mathrm{to} 2 \mathrm{s}$ is 

A box of about $10 \mathrm{kg}$is placed at point A on a horizontal surface. It is moved to point B which is at a distance of  $2 \mathrm{m}$ from A by the action of force, $4 \mathrm{N}$applied on the box at an angle of $60°$.
(a) Find the work done by the gravitational force on the box. 
(b) Calculate the work done by the externally applied force. Justify your answer. (Given $\mathrm{g}=10 {\mathrm{ms}}^{-2}$) 

A particle is moving uniformly on a horizontal circular path. Work done by centripetal force on the particle in one half revolution is 
 

A particle of mass $40 \mathrm{gm}$ slides along a track with elevated ends and a flat horizontal bottom. At the bottom where the horizontal portion begins a spring is kept. When the particle falls from the height slides and reaches it gets compressed by $19.6 \mathrm{cm}$. What is the spring constant of the spring? Assume that the track and the flat horizontal portion are frictionless.

A particle is moving in the $xy$ plane undergoes a displacement $\overrightarrow{s}=\left(4\hat{i}+6\hat{j}\right) \mathrm{m}$ while a constant force $\overrightarrow{F}=\left(10\hat{i}+3\hat{j}\right) \mathrm{N}$ acts on the particle. What is the work done?

A cricket ball of mass $500 \mathrm{g}$ travelling at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$ is caught by a fielder and in doing so he withdraws his hands back through $40 \mathrm{cm}$. Calculate the work done by him. 

A coolie carries a suitcase weighing $50 \mathrm{kg}$ over his head and travels a distance of $15 \mathrm{m}$ along a vertical direction. Calculate the work done.

A block of mass $50 \mathrm{kg}$ just slides over a distance of $1 \mathrm{m}$. If the coefficient of friction between their surfaces is $0.2$, the work done against friction is

A cubical vessel of height $1 \mathrm{m}$ is full of water. What is the amount of work done in pumping water out of the vessel?

[Take $g=10 {\mathrm{ms}}^{-2}$]

When a force is applied on a moving body, its motion is retarded. Then the work done is

Deduce work energy theorem for constant force.

Explain work.

A force of $\overrightarrow{F}=(2\hat{i}+3\hat{j}+4\hat{k}) N$ is applied on a particle displacing it by a distance $\overrightarrow{\mathrm{d}}=(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}+\hat{\mathrm{k}})\mathrm{m}$. Calculate the work done by the force.

If this lift is moving downward with constant velocity $20 \mathrm{m} {\mathrm{s}}^{-1},$ find work done by tension in $2 \sec$:-

A body of mass $10 \mathrm{kg}$ initially at rest is displaced by $5 \mathrm{m}$ against the of force $100 \mathrm{N}$ acting in the direction opposite to the direction of displacement of the body. What will be the work done by the force on the body?

A body of mass $5 \mathrm{kg}$ initially at rest is displaced by $2 \mathrm{m}$ under the application of force $90 \mathrm{N}$ acting at an angle $\theta$ to the motion of the body. What will be the value of $\theta$ such that the work done on the body by the force will be minimum.

If the momentum of a particle with fixed mass is doubled, its kinetic energy,

Work will said to be done if the force and displacement are

A body constrained to move along y-axis is subjected to a constant force $\overrightarrow{F}=-\widehat{i}+2\widehat{j}+3\widehat{k} \mathrm{N}.$ The work done by this force in moving the body a distance of $4 \mathrm{m}$ along $Y$-axis is _____ $\mathrm{J}$.