A block is moving on an inclined plane making an angle $45^{\circ}$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. If we define $N=10 \ \mu$, then $N$ is

A car is moving with uniform velocity on a rough horizontal road. Therefore, according to Newton's first law of motion

A block of mass $1\, kg$ is at rest on a horizontal table. The coefficient of static friction  between the block and the table is $0.5.$ The magnitude of the force acting upwards at  an angle of $60^o$ from the horizontal that will just start the block moving is

An inclined plane is bent in such a way that the vertical cross-section is given by $y =\frac{ x ^{2}}{4}$ where $y$ is in vertical and $x$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu=0.5,$ the maximum height in $cm$ at which a stationary block will not slip downward is............$cm$

Which one of the following statements is incorrect? 

What is the maximum value of the force $F$ such that the block shown in the arrangement does not move ....... $N$