Shown in the figure is a rigid and uniform one-meter-long rod $AB$ held in a horizontal position by two strings tied to its ends and attached to the ceiling. The rod has a mass $m$ and another weight of mass $2m$ is hung at a distance of $75\, cm$ from $A$. The tension in the string at $A$ is $....mg$.

$A$ horizontal beam is pivoted at $O$ as shown in the figure. Find the mass $m$ to make the scale straight in $kg$.

$A$ car weighs $1800 \, kg$. The distance between its front and back axles is $1.8 \, m$. Its centre of gravity is $1.05 \, m$ behind the front axle. The force exerted by the level ground on each back wheel is ....... $N$.

$A$ uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height $a$ $(a < R)$ by applying a force $F$ at its centre $'O'$ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of $F$ required is

$A$ right triangular plate $ABC$ of mass $m$ is free to rotate in the vertical plane about a fixed horizontal axis through $A$. It is supported by a string at $B$ such that the side $AB$ is horizontal. The reaction at the support $A$ is:

$A$ metre scale is supported on a wedge at its centre of gravity. $A$ body of weight '$W$' is suspended from the $20 \text{ cm}$ mark and another weight of $25 \text{ g-wt}$ is suspended from the $74 \text{ cm}$ mark to balance it, and the metre scale remains perfectly horizontal. Neglecting the weight of the metre scale, the weight of the body is: (in $\text{ g-wt}$)