Question

A cubical block of mass m rests on a rough horizontal surface, $\mu$ is the coefficient of static friction between the block and the surface. A force mg acting on the cube at an angle $\theta$ with vertical side of the cube pulls the block. If the block is to be pulled along the surface then the value cot ( $\theta /2$) is

• A. Less than $\mu$
• B. Greater than $\mu$
• C. Equal to $\mu$
• D. Not dependent on $\mu$

Answer 1

The correct option is B Greater than $\mu$

For balancing the forces:

$Fsin\theta =\mu (mg-Fcos\theta );F=mg$

$\Rightarrow sin\theta /(1-cos\theta )=\mu \Rightarrow cot\left(\theta /2\right)=\mu$

To move the body, $cot\left(\theta /2\right)>\mu$