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InterviewSolution
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A body takes ''n'' times as much time to slide down a rough inclined plane as it takes to slide down an identical but smooth inclined plane. If the angle of inclination of the inclined plane is ''theta''. What is the coefficient of friction between the body and the rough plane ? |
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Answer» Solution :Let be the LENGTH of both the INCLINED planes and `THETA` be the inclination. Then the TIME taken by a body sliding the smooth and rough inclined planes are `t_("smooth")=sqrt((2l)/(g SIN theta))` and`t_("rough")=sqrt((2l)/(g(sin theta - mu_(k)cos theta)))` If `t_("rough")= nt_("smooth")` `sqrt((2l)/(g(sin theta - mu_(k)cos theta)))=n sqrt((2l)/(g sin theta))` On solving we get`mu_(k)=tan theta (1-(1)/(n^(2)))` |
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