$A$ body of mass $10 \ kg$ slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt{3}$. Taking $g = 10 \ m/s^2$,the least force which acts at an angle of $30^\circ$ to the horizontal is ...... $N$.

$A$ body of weight $50 \,N$ is placed on a horizontal surface as shown in the figure. The minimum force required to move the body is $28.28 \,N$. The frictional force and the normal reaction are respectively.

Impending relative motion is opposed by which type of friction?

$A$ block of mass $M$ is placed on a horizontal surface and it is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If $\mu$ is the coefficient of friction between the block $M$ and the horizontal surface,then the minimum value of $m_0$ required to keep the block $m$ stationary is

$A$ block of $1\, kg$ is stopped against a wall by applying a force $F$ perpendicular to the wall. If $\mu = 0.2$,then the minimum value of $F$ will be ....... $N$.

$A$ block of mass $M$ rests on a rough horizontal table. $A$ steadily increasing horizontal force is applied such that the block starts to slide on the table without toppling. The force is continued even after sliding has started. Assume the coefficients of static and kinetic friction between the table and the block to be equal. The correct representation of the variation of the frictional force $f$,exerted by the table on the block with time $t$ is given by