Question

A uniform 240g meter stick can be balanced by a 240g weight placed at the 100cm mark if the fulcrum is placed at the point marked as
a.75cm
b.60cm
c.50cm
d.40cm
The answer is A but I need the solution.

Answer 1

a.75cm

Explanation:

Given;

mass of uniform meter stick, $m=0.24\ kg$

mass of balance weight, $m'=0.24\ kg$

position of the balance weight, $x=100\ cm=1\ m$

length of the stick, $l=1\ m$

As the meter stick is uniform then the mass is concentrated at the mid point i.e. at 50 cm.

Now using the balancing of moments, let the fulcrum be positioned at distance d meters from the balance mass.

then,

$m'.g.(1-d)=m.g.(d+0.5)$

$0.24\times9.8\times (1-d)=0.24\times 9.8\times (0.5+d)$

Since the fulcrum is positioned at a point before the balance mass and beyond the center of mass of the stick.

$d=0.25\ m=25\ cm$

So the position of fulcrum is 0.75 meter from the balance mass.

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TOPIC: moment

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