Question

A small block on a rough inclined plane inclined at an angle of ${30}^{\circ }$ with certaind acceleration. When the inclination of the plane is increase to${60}^{\circ }$ the acceleration is found doubled. The coefficient of friction between the plane and the block is nearly

• A. 0.11
• B. 0.55
• C. 0.65
• D. 0.41

Answer 1

The correct option is A 0.11

$\begin{array}{c}g\sin {30}^0-\mu g\sin {30}^0=a\\ g\sin {60}^0-\mu g\sin {60}^0=2a\\ \Rightarrow g\sin {60}^0-\mu g\cos {60}^0=2g\sin {30}^0-2\mu g\cos {30}^0\\ \Rightarrow \frac{\sqrt{3}}{2}-\frac{\mu }{2}=1-\sqrt{3}\mu \\ \Rightarrow 1-\frac{\sqrt{3}}{2}=\left(\sqrt{3}-\frac{1}{2}\right)\mu \\ \Rightarrow \frac{2-\sqrt{3}}{2\sqrt{3}-1}=\mu \\ \Rightarrow \mu \simeq 0.11\\ Hence,\\ optionAiscorrectanswer.\end{array}$