A body of mass 'm' is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt[]{x}}{5}$ if the time of ascent is half of the time of descent. The value of x is__________.

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Vishal Baghel | Contributor-Level 10

6 months ago

For ascent

$t_{a} = \sqrt[]{\frac{2 l}{a_{a s c e n t}}} = \sqrt[]{\frac{2 l}{g (s i n θ + μ c o s θ)}}$

For descent

$t_{d} = \sqrt[]{\frac{2 l}{a_{d e s c e n t}}} = \sqrt[]{\frac{2 l}{g (s i n θ - μ c o s θ)}}$

According question, we can write

$\Rightarrow μ = \frac{3}{5} t a n θ = \frac{3}{5} t a n 30 ° = \frac{\sqrt[]{3}}{5}$

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A body of mass 'm' is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is x 5 if the time of ascent is half of the time of descent. The value of x is__________.

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