Question

A particle is projected along a rough plane inclined at an angle of ${45}^o$ with the horizontal. if the coefficient of friction is $\frac{1}{2}$, then the retardation is-

• A. $\frac{g}{2}$
• B. $\frac{g}{\sqrt{2}}$
• C. $\frac{g}{\sqrt{2}}(1+\frac{1}{2})$
• D. $\frac{g}{\sqrt{2}}(1-\frac{1}{2})$

Answer 1

The correct option is C $\frac{g}{\sqrt{2}}(1+\frac{1}{2})$

• weight component along down the incline is $mgsin{45}^0$ and friction down the incline is$\mu mgcos{45}^0$
• adding both and dividing by mass $m$ we will get the net retardation means acceleration downward $a=gsin{45}^0+\mu gcos{45}^0$= $\frac{3g}{2\sqrt[2]{22}}$ so option C is correct.