Question 6(i)A uniform meter scale of mass 60 g, carries masses of 20 g, 30 g and 80 g from points 10 cm, 20 cm and 90 cm marks. Where must be the scale hanged with string to balance the scale?

Question

Accepted Answer

Let, D be the point from where the scale is hanged so that the meter scale and the various masses are balanced.

A uniform meter scale of mass 60 g, carries masses of 20 g, 30 g and 80 g from points 10 cm, 20 cm and 90 cm marks. Where must be the scale hanged with string to balance the scale? Physics Sample Paper Solved ICSE Class 10.

Clockwise moments = 80 x GD

Anticlockwise moments = (20 x FD) + (30 x ED) + (60 x CD)

As the meter scale is balanced.

∴ Sum of clockwise moments = sum of anticlockwise moments

80 x GD = (20 x FD) + (30 x ED) + (60 x CD)

[80 x {90 - (50 + x)}] = [20 x (50 + x - 10)] + [30 x (50 + x - 20)] + 60x

[80 x (90 - 50 - x)] = [20 x (50 + x - 10)] + [30 x (50 + x - 20)] + 60x

[80(40 - x)] = [20(40 + x)] + [30(30 + x)] + 60x

3200 - 80x = 800 + 20x + 900 + 30x + 60x

3200 - 80x = 1700 + 110x

3200 - 1700 = 110x + 80x

1500 = 190x

x = $\dfrac{1500}{190}$ = 7.89 ≈ 7.9 cm

Hence, the string should be hanged at 50 + 7.9 = 57.9 cm mark.

Solved Sample Paper 3 — Question 7

Question 6(i)