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Overall Equilibrium

For the figur...

Question

For the figure shows, a rod of mass $10 k g$ (of length 1 $00 c m$ ) with some point masses tied to it at different positions. Find the distance of the point (from $A$ ) at which if the rod is picked over a knife edge, it will be in equilibrium about that knife

26.32 c m

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28.72 c m

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30.43 c m

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32.50 c m

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Solution

The correct option is A $26.32 c m$
Let distance from A at which the knife is pricked be $x c m$
For Rotational equilibrium balancing torques of masses about the knife's axis we get :
$20 x + 15 (x - 20) = 5 (100 - x - 5) + 7.5 (100 - x - 20)$
(Magnitude of Torque $=$ Force $\times$ perpendicular distance )
On soving ,
$x = 26.32 c m$

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For the figure shows, a rod of mass 10kg (of length 100 cm) with some point masses tied to it at different positions. Find the distance of the point (from A) at which if the rod is picked over a knife edge, it will be in equilibrium about that knife

For the figure shows, a rod of mass $10 k g$ (of length 1 $00 c m$ ) with some point masses tied to it at different positions. Find the distance of the point (from $A$ ) at which if the rod is picked over a knife edge, it will be in equilibrium about that knife