Question

A uniform meter rule balances horizontally on a knife edge placed at the $58$ cm mark when a weight of $20$ gf is suspended from one end.

Answer 1

Let, $W$ be the mass of uniform scale,

When the edge is placed at $58cm$ mark and $20g$ weight suspended at one end, then uniform scale would be balaced.

Applying here the principle of moments:

The uniform scale weight would be balanced at mid point i.e. $50cm$ of the scale.

A weight of $20g$ is placed at $58cm$ mark.

So the clockwise moment due to mass of the scale will be $W(50-42)=8W$

The anticlockwise moment due to mass $20g$ will be $20\times (50-8)=840.$

For equilibrium, clockwise moment = anticlockwise moment

So,

$Wx8=840$

$W=105g$

The wight of the uniform meter $=105g.$