Question

a uniform metre scale is balanced at 40 cm mark when weights of 20gf and 5gf are suspended at 5 CM mark respectively calculate the weight of metre scale

Answer 1

Denote one end by A and the other by C, let the point of balance be denoted by B.

m - smaller mass;        WmWm- weight of smaller mass

M - larger mass;          WM−WM− weight of larger mass

s - mass of the scale;  Ws−Ws−weight of scale

AB = 0.4m

WmWmto B = 0.3m

WMWM to B = 0.2m

B to WsWs= 0.1m

For the scale to balance: ∑moments (counter-clockwise) = ∑moments (clockwise)

∑moments (clockwise) = (0.1)Ws(0.1)Ws

∑moments (counter-clockwise)=(0.3)Wm+(0.2)WM=(0.3)Wm+(0.2)WM

=(0.3)mg+(0.2)Mg=(0.3)mg+(0.2)Mg

=g(0.3m+0.2M)=g(0.3m+0.2M)

∑moments (counter-clockwise) = ∑moments (clockwise)

(0.1)Ws(0.1)Ws=g(0.3m+0.2M)=g(0.3m+0.2M)

Ws=g(0.3m+0.2M)/0.1Ws=g(0.3m+0.2M)/0.1

using g=9.81,m=0.1kgg=9.81,m=0.1kg and  M=0.2kgM=0.2kg

Ws=6.867N