Question

A body is sliding down an inclined plane having coefficient of friction 0.5. The normal reaction is twice that of resultant downward force along the inclined plane. The angle between the inclined plane and the horizontal is..

• A. ${30}^{\circ }$
• B. ${37}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

$\mu =0.5,N=\text{mg cos}\theta N=2\text{F}=2\text{mg}(\text{sin}\theta -\mu \text{cos}\theta )N=\text{mg}\text{cos}\theta \text{cos}\theta =2\text{cos}\theta (\text{tan}\theta -\mu )\frac{1}{2}=\text{tan}\theta -\frac{1}{2}\Rightarrow tan\theta =1\Rightarrow \theta ={45}^o$