A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is $\mu .$ If the mass is pulled by a force $P$ as shown in the figure, the limiting friction between body and surface will be
$\mu mg$
$\mu \,\left[ {mg + \left( {\frac{P}{2}} \right)} \right]$
$\mu \,\left[ {mg - \left( {\frac{P}{2}} \right)} \right]$
$\mu \,\left[ {mg - \left( {\frac{{\sqrt 3 \,P}}{2}} \right)} \right]$
A coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre $............\,cm$
A uniform rope lies on a horizontal table so that a part of it hangs over the edge. The rope begins to slide down when the length of the hanging part is $25\%$ of the entire length. The coefficient of friction between the rope and the table is
In the given figure the acceleration of $M$ is $(g = 10 \,ms^{-2})$
A block of mass $m$ is stationary on a rough plane of mass $M$ inclined at an angle $\theta$ to the horizontal, while the whole set up is accelerating upwards at an acceleration $\alpha$. If the coefficient of friction between the block and the plane is $\mu$, then the force that the plane exerts on the block is
A uniform rod of length $L$ and mass $M$ has been placed on a rough horizontal surface. The horizontal force $F$ applied on the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation $\mu = Kx$ where $K$ is a $+$ ve constant. Then the tension at mid point of rod is