Question

A metre scale is balanced on a knife-edge at its centre. When a mass of 10 kg is kept at the 12 cm mark, the scale is balanced at 45 cm. What is the mass of the metre scale?
A. 56 g
B. 76 g
C. 86 g
D. 66 g

Answer 1

In a balanced state, the product of weight of mass kept on a scale and the distance between the balanced point of the scale and point at which it is kept is equal to the product of weight of scale and distance between centre and the point at which scale is balanced.

Complete step by step answer:
A metre scale is kept on a knife-edge at its centre and it is balanced at 45 cm when a mass m of 10 kg is placed at the 12 cm mark. Let M be the mass of the metre scale. A metre rule has the same distribution of mass throughout its length, so its weight Mg (g is acceleration due to gravity) will act at its middle point i.e., at the 50 cm mark.
According to the principle of moments, the sum of the anticlockwise moments is equal to the sum of the clockwise moments in an equilibrium i.e., in a balanced state. A physical balance works on the principle of moments. The anticlockwise moment in this case indicates the turning effect of force due to the weight of mass m in an anticlockwise direction and clockwise moment is defined as the weight of scale tends to turn the scale clockwise.
From the principle of moments,
Anticlockwise moment (due to mass m) = Clockwise moment (due to mass M)
$mg\left( {45 - 12} \right) = Mg\left( {50 - 45} \right)$
$\implies 10 \times 33 = M \times 5$
$\implies M = \dfrac{{330}}{5}$
$\therefore M = 66g$

So, the correct answer is “Option D”.

Note:
The mass m is kept on the left side of the scale which tends to turn the scale in an anticlockwise direction and weight of the scale tends to rotate it in a clockwise direction and both the weights are balanced in equilibrium.