Work Energy and...

A particle moves along $$X-$$axis from $$x=0$$ to $$x=1\ m$$ under the influence of a force given by $$F=3x^{2}+2x-10$$. Work done in the process is:

A block of mass $$m$$ at the end of a string is whirled round in a vertical circle of radius $$R$$. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is:

$$4\ J$$ of work is required to stretch a spring through $$10\ cm$$ beyond its unstreched length. The extra work required to stretch it through additional $$10\ cm$$ shall be

Under the action of a force, a $$2\ kg$$ body moves such that its position $$x$$ as a function of time $$t$$ is given by $$x=\dfrac{t^{3}}{3}$$, where $$x$$ is in meter and $$t$$ in second. The work done by the force in first two seconds is:

A particle moves along $$x-$$axis from $$x=0$$ to $$x=5$$ meter under the influence of a force $$F=7-2x+3x^{2}$$. The work done in the process is:

A boy is swinging in a swing. If he stands the time period will

A body of mass $$4\ kg$$ moves under the action of a force $$\overrightarrow { F } =\left( \hat { 4i } +12{ t }^{ 2 }\hat { j }  \right) N$$, where $$t$$ is the time in second. The initial velocity of the particle is $$(2\hat { i } +\hat { j } +2\hat { k } )m{s}^{-1}$$. If the force is applied for $$1\ s$$, work done is:

Under the action of a force, a $$2lg$$ body moves such that it position $$x$$ as a function of time is given by $$x=\cfrac{{t}^{3}}{3}$$, where $$x$$ is in metre and $$t$$ in seconds. The work done by the force in the first two seconds is

A particle is moving in a vertical circle the tension in the string when passing through two position at angle $${30}^{o}$$ and $${60}^{o}$$ from vertical lowest position are $${T}_{1}$$ and$${T}_{2}$$ respectively then-

A weightless thread can support tension upto $$30N$$. A particle of mass $$0.5kg$$ is tied to it and is revolved in a circle of radius $$2m$$ in a vertical plane. If $$g=10m/{s}^{2}$$, then the maximum angular velocity of the stone will be