Question

A box when dropped from a certain height reaches the ground with a speed $v$. When it skids from rest from the same height down a rough inclined plane inclined at an angle ${45}^{\circ }$ to the horizontal, it reaches the ground with a speed $\frac{v}{3}$. The coefficient of sliding friction between the box and the plane is (acceleration due to gravity is $10m{s}^{-2}$ )

• A. $\frac{8}{9}$
• B. $\frac{1}{9}$
• C. $\frac{2}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A

$\frac{8}{9}$

Case-1

$v=\sqrt{2gh}$

Case-2

$\Delta U+\Delta k=W_f$

$-mgh+\frac{1}{2}m\left(\frac{2gh}{9}\right)=-\mu mgh$

$\Rightarrow \mu =\frac{8}{9}$