Please solve the following question and also tell the Dimensions of b ?

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1 Answer
Sep 23, 2017

Given that the mass of the rotating particle is #m# and the resistive frictional force acting on it is #F_("fric")=3bv^2#, where #v# represents instantaneous speed of the particle,

Hence its instantaneous retardation will be

#-(dv)/(dt)=F_"fric"/m=(3bv^2)/m#

#=>-(dv)/v^2=(3b)/mdt#

#=>-int(dv)/v^2=(3b)/m intdt#

#=>1/v=(3b)/m t+c#, where c= integration constant

Now it is given that at #" "t= 0 ,v=v_0#

So #c=1/v_0#

So the relation becomes

#=>1/v=(3b)/m t+1/v_0#

It is also given that at #t=t_0, v=v_0/3#

#=>3/v_0=(3b)/m t_0+1/v_0#

So #t_0=(2m)/(3bv_0)#

Again #b==(2m)/(3t_0v_0)#

So dimension of #b="dimension of mass"/("dimension of time"xx "dimension of velocity" #

#=([M])/([T][LT^-1])=[ML^-1]#