A rod of mass $1\ kg$ , length $1\ m$ is suspended horizontally with the help of two ideal strings as shown in figure. First a mass is suspended to the left most end keeping rod horizontal, than a second mass is suspended to the right most end again keeping horizontal orientation. The maximum total mass that can be suspended in that way keeping horizontal orientation of rod ....... $kg.$
$3$
$6$
$2$
$9$
$A$ body weighs $6$ gms when placed in one pan and $24$ gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is ....... $gm$.
Persons $A$ and $B$ are standing on the opposite sides of a $3.5 \,m$ wide water stream which they wish to cross. Each one of them has a rigid wooden plank whose mass can be neglected. However, each plank is only slightly longer than $3 \,m$. So, they decide to arrange them together as shown in the figure schematically. With $B$ (mass $17 \,kg$ ) standing, the maximum mass of $A$, who can walk over the plank is close to ............ $kg$
$A$ man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support $A$ with distance $x$ of the man from the end of the plank is best represented by :
Two vertical walls are separated by a distance of $2\ m$. Wall $A$ is smooth while wall $B$ is rough with a coefficient of friction $0. 5$. A uniform rod is placed between them as shown. The length of longest rod that can be placed between walls is equal to
A non-uniform bar of weight $W$ is suspended at rest by two strings of negligible weight as shown in Figure. The angles made by the strings with the vertical are $36.9^{\circ}$ and $53.1^{\circ}$ respectively. The bar is $2\; m$ long. Calculate the distance $d$ of the centre of gravity of the bar from its left end.