Factors Affecting Friction Force

Q. While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure

1. larger coefficient of friction
2. smaller coefficient of friction
3. larger normal force
4. smaller Normal force

Q. A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force $P$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $P$ is varied from $P_1=mg(\sin \theta -\mu \cos \theta )$ to $P_2=mg(\sin \theta +\mu \cos \theta )$, the frictional force $f$ versus $P$ graph will look like:

1. 
2. 
3. 
4. 

Q. A block of mass $m$ is placed on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force $P$ parallel to the inclined plane. The direction of force pointing up the plane is taken to be positive. As force $P$ is varied from $P_1=mg(\sin \theta -\mu \cos \theta )$ to $P_2=mg(\sin \theta +\mu \cos \theta )$, then the graph of frictional force $f$ versus $P$ graph will look like:

1. 
2. 
3. 
4.