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4-1.Newton's Laws of Motion
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In the above question the speed of the mass when travelled half the maximum distance is
A
$\sqrt{\frac{g \tan \theta \sin \theta}{\mu_0}}$
B
$\sqrt{\frac{g \tan \theta \sin \theta}{2 \mu_0}}$
C
$\sqrt{\frac{g \tan \theta \sin \theta}{8 \mu_0}}$
D
none of these
Solution
$\int \limits_0^{x / 2} g\left(\sin \theta-\mu_0 x \cos \theta\right) d x=\int \limits_0^v v d v$
$g\left[\sin \theta \cdot \frac{x}{2}-\frac{\mu_0}{2}\left(\frac{x}{2}\right)^2 \cos \theta\right]=\frac{v^2}{2}$
Keeping the value
$x=\frac{2}{\mu_0} \tan \theta$
$v=\sqrt{\frac{g \tan \theta \sin \theta}{\mu_0}}$
Standard 11
Physics
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