Physics - W.E.P. Question with Solution | TestHub

Mass of hanging part $=\frac{\mathrm{M}}{4}$ Depth of centre of mass from level of table $=\frac{\mathrm{L}}{8}$ Hence, work required to pull hanging part to table = change in gravitational P.E. $=\left(\frac{\mathrm{M}}{4}\right)\mathrm{g}\left(\frac{\mathrm{L}}{8}\right)=\frac{\mathrm{MgL}}{32}$ Alternate Solution :

Consider an element dx at a distance x from table level. work required to pull element to table

$$\begin{array}{rlr}& \mathrm{dw}=(\mathrm{dm})\mathrm{g}(\mathrm{x})& \mathrm{dw}=\left(\frac{\mathrm{M}}{\mathrm{L}}\mathrm{dx}\right)\mathrm{gx}\end{array}$$

Hence, work required to pull element to table

$$\begin{array}{rlrl}& \mathrm{w}=\int \mathrm{dw}={\int }_0^{\mathrm{L}/4}\frac{\mathrm{M}}{\mathrm{L}}\mathrm{gx}\mathrm{dx}& \mathrm{w}=\frac{\mathrm{Mg}}{\mathrm{L}}{\left[\frac{{\mathrm{x}}^2}{2}\right]}_0^{\mathrm{L}/4}& \mathrm{w}=\frac{\mathrm{MgL}}{32}\end{array}$$