Question

A box when dropped from a certain height reaches the ground with a speed v. When it skides from rest from the same height down a rough inclined at in angle 45 to the horizontal,it reaches the ground with a speed v/3. The coefficient of sliding friction between the box and the plan 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

$△U+△kE=w_f$

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

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