Name: Centre of Mass and Centre of Gravity
Uploaded: 2019-07-19
Duration: 3 min 59 s
Description: Centre of gravity and centre of mass. Are they the same, or is there a difference between the two? Let’s find out in this interesting video!

Question

The diagram shows a uniform metre rule weighing

100 gf

, pivoted as its centre

O

. Two weights

150 gf

and

250 gf

hang from the points

A

and

B

of the metre rule such that

O A = 40 cm

and

O B = 20 cm

. Calculate
(i) the total anticlockwise moment about

O

.
(ii) the total clockwise moment about

O

.
(iii) the difference of anticlockwise and clockwise moments.
(iv) the distance from

O

where a

100 gf

weight should be placed to balance the metre rule.

Accepted Answer

(i) The weight at $A$ produces anticlockwise moment about the point $O$ .
The total anticlockwise moment about $O$
$= 150 gf \times 40 cm = 6000 gf cm$

ii) The weight at $O B = 20 cm$ produces clockwise moment about the point $O$ .
The total clockwise moment about $O$
$= 250 gf \times 20 cm = 5000 gf cm$

(iii) Anticlockwise moments are taken positive and clockwise moments are taken negative.
The difference between anticlockwise and clockwise moments
$= 6000 - 5000 = 1000 gf cm$

(iv) Since the anticlockwise moment is greater than the clockwise moment, the $100 gf$ weight should be placed on the right side of the point $O$ to produce clockwise moment and balance the metre rule. Let $d$ be the distance of the $100 gf$ from $O$ .

According to the principle of moments, at equilibrium,
Sum of anticlockwise moments = Sum of clockwise moments
$150 gf \times40 cm = (250 gf \times20 cm) + (100 gf \times d)$
$100 d = (150 \times 40) - (250 \times 20)$
$d = \frac{6000 - 5000}{100}$
$d = 10 cm$

Therefore, the $100 gf$ should be placed at a distance of $10 cm$ from the right of the point $O$ .

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