Question

A particle is projected along a line of greatest slope on a rough plane inclined at an angle of $45^{\circ }$ with the horizontal. If the coefficient of friction is $\frac{1}{2}$ , then the retardation is

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

Answer 1

Answer: (C)

The acceleration of the body on the incline is
$a=g\left(sin\theta +\mu cos\theta \right)$
$a=g\left(sin45^{\circ }+\frac{1}{2}\times cos45^{\circ }\right)$
$a=g\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\times \frac{1}{\sqrt{2}}\right)$
$a=\frac{g}{\sqrt{2}}\left(1+\frac{1}{2}\right)$
$a=\frac{3g}{2\sqrt{2}}$