Question

A box is projected along a line of greatest slope up a rough plane inclined at an angle of ${45}^{\circ }$ with the horizontal. If the coefficients of friction is $1/2$, then the retardation is:-

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

Answer 1

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

Let $a$ be the retardation of the block.
from FBD, $ma=mg\sin \theta +f=mg\sin \theta +\mu mg\cos \theta$
or $a=g(\sin 45+\frac{1}{2}\cos 45)$
or $a=g(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\times \frac{1}{2})$
or $a=g\frac{(1+\frac{1}{2})}{\sqrt{2}}$