In a physical balance working on the principle of moments, when $5\, mg$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
Left arm is longer than the right arm
Both the arms are of same length
Left arm is shorter than the right arm
Every object that is weighed using this balance appears lighter than its actual weight
A uniform rod of length $1\, m$ and mass $4\, kg$ is supported on two knife-edges placed $10 \,cm$ from each end. A $60\, N$ weight is suspended at $30\, cm$ from one end. The reactions at the knife edges is
Two light vertical springs with equal natural lengths and spring constants $k_1$ and $k_2$ are separated by a distance $l$. Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $AB$. $A$ vertical downwards force $F$ is applied at point $C$ on the rod. $AB$ will remain horizontal in equilibrium if the distance $AC$ is
A smooth rod of length $l$ is kept inside a trolley at an angle $\theta$ as shown in the figure. What should be the acceleration a of the trolley so that the rod remains in equilibrium with respect to it?
A uniform meter scale is supported from its $20\ cm$ mark. A body suspended from $10\ cm$ mark keeps the scale horizontal. However, the scale gets unbalanced if the body is completely immersed in water. To regain the balance the body is shifted to the $8\ cm$ mark. Therefore, the specific gravity of the material of the body is
$ABC$ is an equilateral triangle with $O$ as its centre. $\vec F_1, \vec F_2 $and $\vec F_3$ represent three forces acting along the sides $AB, BC$ and $AC$ respectively. If the total torque about $O$ is zero then the magnitude of $\vec F_3$ is