Two men are carrying a uniform bar of length $L$, on their shoulders. The bar is held horizontally such that younger man gets $(1/4)^{th}$ load. Suppose the younger man is at the end of the bar, what is the distance of the other man from the end

$A$ 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 ....... $gm$.

A uniform meter scale balances at the $40\,cm$ mark when weights of $10\,g$ and $20\,g$ are suspended from the $10\,cm$ and $20\,cm$ marks. The weight of the metre scale is ...... $g$

$A$ 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 such that the side $AB$ is horizontal. The reaction at the support $A$ is:

A thin rod $MN$, free to rotate in the vertical plane about the fixed end $N$, is held horizontal . When the end $M$ is released the speed of this end, when the rod makes an angle $\alpha $ with the horizontal, will be proportional to ( see figure)

A disc of radius $5\, m$ is rotating with angular frequency $10\, rad / sec .$ A block of mass $2\, kg$ to be put on the disc friction coefficient between disc and block is $\mu_{ k }=0.4,$ then find the maximum distance from axis where the block can be placed without sliding (in $cm$)