Question

23. Find the weight of a metre scale balanced a 30cm mark such that two weights one of 80gf and 10gf are suspended at 5cm mark and 40cm mark respectively.
(a) 10gf (b) 105gf (C) 25gf (d) 32.5gf​

Answer 1

Answer:

Let the meter scales is balanced at X cm mark on the scale.

At the balancing condition, Anticlock wise moment must be equal to clock wise moment.

Clockwise moment, about the balancing point is

= moment by 80  

Answer 2

Given: A metre scale balanced a 30cm mark such that two weights one of 80gf and 10gf are suspended at 5cm mark and 40cm mark respectively.

To find: The weight of the metre scale.

Solution:

• Let the weight of the metre scale be equal to x.
• The weight of the metre scale can be calculated as follows.

        $(f - m_{1}) w_{1} = w_{2} x + (m_{2} - f) w_{2}$

• Here, f is the mark at which the scale is balanced, m₁ is the mark on one side of the balance where the weight is suspended, w₁ is the weight suspended at m₁, m₂ is the mark on the other side of the balance where the weight is suspended, w₂ is the weight suspended at m₂.

        $(30 - 5) 80 = 10x + (40 - 30) 10$

         $x = 190 gf$

Therefore, the weight of the metre scale is 190 gf.