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
$m(g+a)$ upwards
$m g \cos \theta$ normal to the plane
resultant of $m g \cos \theta$ normal to the plane and $\mu m g \cos \theta$ along the plane
resultant of $m(g+a) \cos \theta$ normal to the plane and $\mu m g \cos \theta$ along the plane
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 $............\,cm$
Impending relative motion is opposed by which type of friction ?
A body of mass $1\, kg$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $F\, N$. The value of $F$ will be the Nearest Integer) [Take $g =10 \,ms ^{-2}$ ]
A lift is moving downwards with an acceleration equal to acceleration due to gravity. $A$ body of mass $M$ kept on the floor of the lift is pulled horizontally. If the coefficient of friction is $\mu $, if the lift is moving upwards with a uniform velocity, then the frictional resistance offered by the body is
A heavy box is to dragged along a rough horizontal floor. To do so, person $A$ pushes it at an angle $30^o$ from the horizontal and requires a minimum force $F_A$, while person $B$ pulls the box at an angle $60^o$ from the horizontal and needs minimum force $F_B$. If the coefficient of friction between the box and the floor is $\frac{{\sqrt 3 }}{5}$ , the ratio $\frac{{{F_A}}}{{{F_B}}}$ is