$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $m$ and side $a$,which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between the lines of action of $mg$ and the normal reaction $N$ is:

Which of the following statements is not true?

$A$ body of mass $2 \,kg$ is acted upon by two forces each of magnitude $1 \,N$, making an angle of $60^{\circ}$ with each other. The net acceleration of the body (in $m/s^2$) is

$A$ block of mass $5\,kg$ starting from rest is pulled up on a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal with an effective acceleration of $1\,m/s^2$. The power delivered by the pulling force at $t = 10\,s$ from the start is $.....\,W$. [Use $g = 10\,m/s^2$] (calculate the nearest integer value).

The masses of blocks $A$ and $B$ are $m$ and $M$ respectively. Between $A$ and $B$,there is a constant frictional force $F$ and $B$ can slide on a smooth horizontal surface. $A$ is set in motion with velocity $v_0$ while $B$ is at rest. What is the distance moved by $A$ relative to $B$ before they move with the same velocity?

$A$ $\sqrt{34}\,m$ long ladder weighing $10\,kg$ leans on a frictionless wall. Its feet rest on the floor $3\,m$ away from the wall as shown in the figure. If $F_{f}$ and $F_{w}$ are the reaction forces of the floor and the wall,then the ratio of $F_{w}/F_{f}$ will be:
(Use $g=10\,m/s^{2}$)