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Q)

A block of mass m is being pulled up a rough inclined by an agent delevering constant power P. The coefficient of friction between block and incline is $\mu$. The maximum speed of the block during the course of ascent is

$ a)\; \large\frac{P}{mg \sin \theta+\mu mg \cos \theta} \\ b)\; \large\frac{P}{mg \sin \theta-\mu mg \cos \theta} \\ c) \;\large\frac{2P}{mg \sin \theta-\mu mg \cos \theta} \\ d)\; \large\frac{3P}{mg \sin \theta-\mu mg \cos \theta}$

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A)
$a=\large\frac{dv}{dt}$
Force due to power P is
$F=\large\frac{p}{v}$$;f=\mu R$
$F-mg \sin \theta-\mu R=ma$
$\large\frac{P}{v}$$-mg \sin \theta - \mu mg \cos \theta=m \large\frac{dv}{dt}$
Velocity is maximum when $\large\frac{dv}{dt}$$=0$
$\large\frac{P}{v_{\Large max}}$$= mg \sin \theta +\mu mg \cos \theta$
$v_{max}= \large\frac{P}{mg \sin \theta+\mu mg \cos \theta}$
Hence a is the correct  answer

 

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