A body of mass 'm' is launched up on a rough inclined plane making an angle of 30$^\circ$ with the horizontal. The coefficient of friction between the body and plane is ${{\sqrt x } \over 5}$ if the time of ascent is half of the time of descent. The value of x is __________.
Answer (integer)
3
Solution
${t_a} = {1 \over 2}{t_d}$<br><br>$\sqrt {{{2s} \over {{a_a}}}} = {1 \over 2}\sqrt {{{2s} \over {{a_d}}}}$ ..... (i)<br><br>${a_a} = g\sin \theta + \mu g\cos \theta$<br><br>$= {g \over 2} + {{\sqrt 3 } \over 2}\mu g$<br><br>${a_d} = g\sin \theta - \mu g\cos \theta$<br><br>$= {g \over 2} - {{\sqrt 3 } \over 2}\mu g$<br><br>using the above values of a<sub>a</sub> and a<sub>d</sub> and putting in equation (i) we will gate $\mu = {{\sqrt 3 } \over 5}$
About this question
Subject: Physics · Chapter: Laws of Motion · Topic: Newton's First Law
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