Question

A body is given a velocity $\sqrt{2gr}$ at the highest point of a half circular smooth track which is joined by a rough horizontal track whose co-efficient of friction is $\mu =\mathrm{0.5.}$ Then the distance traveled by the particle before it stops on horizontal track is (Given acceleration due to gravity$=g$)

• A. $1m$
• B. $4m$
• C. $6m$
• D. none of these

Answer 1

The correct option is C $6m$

Using work energy theorem
Work done by friction$=$K.E + P.E.
$\therefore 0.5\times mgd=\frac{1}{2}m(\sqrt{2gr}{)}^2+mg\times 2r$
$0.5\times mgd=mgr+2mgr$
$0.5\times mgd=3mgrd=6\times r=6m$