Physics - NLM Question with Solution | TestHub

Acceleration of block while sliding down upper half $=\mathrm{g}\sin \varphi$ retardation of block while sliding down lower half $=-(\mathrm{g}\sin \varphi -\mu \mathrm{g}\cos \varphi )$ For the block to come to rest at the bottom, acceleration in I half = retardation in II half. $\mathrm{g}\sin \varphi =-(\mathrm{g}\sin \varphi -\mu \mathrm{g}\cos \varphi )$ $\Rightarrow \mu =2\tan \varphi$ Alternative method: According to work-energy theorem, $\mathrm{W}=\Delta \mathrm{K}=0$ (Since initial and final speeds are zero) $\therefore$ Work done by friction $+$ Work done by gravity $=0$ i.e., $-(\mu \mathrm{mg}\cos \varphi )\frac{\ell }{2}+\mathrm{mg}\ell \sin \varphi =0$ or $\frac{\mu }{2}\cos \varphi =\sin \varphi$ or $\mu =2\tan \varphi$