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An object of mass `m` is tied to a string of length `l` and a variable force F is applied on it which brings the string gradually at angle thit `theta` with the vertical. Find the work done by the force `F` . |
Answer» The various forces involved in the problem are shown in figure. As the object is in equilibrium at every stage, therefore, `mg=Tcostheta and F=Tsin theta` `(F)/(mg)=(Tsintheta)/(Tcostheta)=tantheta` `F=mg tan theta` ….(i) Work done by the force, `W=int_(0)^(theta)vecF.dvecs=int_(0)^(theta)F ds cos theta` `=int_(0)^(theta)mg tantheta xx(ld theta). costheta` `=mgl int_(0)^(theta)sind theta=mgl[-costheta]_(0)^(theta)` `=-mgl(cos theta-cos 0^(@))` `W=mgl(1-costheta)` |
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