Question

A particle is projected up along a rough plane of inclination ${45}^0$ with the horizontal. If the coefficient of friction is 0.5, the retardation is (g $=$ acceleration due to gravity):

• A. $\frac{g}{2}$
• B. $\frac{g}{2\sqrt{2}}$
• C. $\frac{3g}{2\sqrt{2}}$
• D. $\frac{g}{\sqrt{2}}$

Answer 1

The correct option is C $\frac{3g}{2\sqrt{2}}$

Equating forces along X and Y axes,
where $mgsin\theta$ is the parallel component of weight and $mgcos\theta$ is the normal component
$N=mgcos\theta$
Also,
$F=mgsin\theta +{\mu }_{k}mgcos\theta$
$\therefore a=gsin\theta +{\mu }_{k}gcos\theta$
$\therefore a=g(sin{45}^o+0.5cos{45}^o)$
$\therefore a=\frac{3g}{2\sqrt{2}}$