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To solve this problem, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments.

Let's assume that the unknown mass is M grams.

The mass of the meter scale is 140 grams, and its center of mass is at a distance of 49.5 cm from the support point. The knife edge used to support the scale has a mass of 20 grams.

When an unknown mass is hanging at a distance of 19.5 cm, the scale is balanced. Let's calculate the clockwise and anticlockwise moments at this point.

The clockwise moment is given by the product of the mass (M) and its distance from the support point (19.5 cm). So, the clockwise moment is 19.5M.

The anticlockwise moment is the sum of the moments of the scale and the knife edge. The moment of the scale is the product of its mass (140 grams) and its distance from the support point (49.5 cm). So, the moment of the scale is 140 * 49.5 = 6,930 grams-cm.

The moment of the knife edge is the product of its mass (20 grams) and its distance from the support point (49.5 cm). So, the moment of the knife edge is 20 ×49.5 = 990 grams-cm.

The total anticlockwise moment is the sum of the moments of the scale and the knife edge, which is 6,930 + 990 = 7,920 grams-cm.

According to the principle of moments, the sum of the clockwise moments is equal to the sum of the anticlockwise moments. So, 19.5M = 7,920.

Let's solve for M:

M = 7,920 / 19.5 = 406.15 grams.

Therefore, the value of the unknown mass is approximately 406.15 grams.

:)