Illustrate a half-meter wooden ruler, pivoted at the 15cm mark and is maintaining a horizontal balance. On the left side, at the 2cm mark, there's a small silver weight, appearing to be around 40 grams, pulling the ruler downwards. The overall mood of the image is calming, with soft, indirect lighting and a blurred, neutral-colored background that doesn't distract but adds depth.

A uniform half metre rule is freely pivoted at the 15cm Mark and it balanced horizontally when a body of mass 40g is hung from the 2cm Mark. calculate the mass of the rule

Draw a clear force diagram of the arrangements

Since a meter is 1m long which z equal to 100cm,,the half meter rule(simple calculation) is 0.5m or 50cm. Hence,we will b working with the 50cm rule.

Now, the center of mass of a 50cm rule is at 25cm.furthermore,from the data we're told that the object is pivoted at 15cm and the object of 40g is hung at 2cm from the beggining of the rule, hence using the simple formula we will relate the two scenarios which are;
Distance from 2cm to where the pivot is multiplied by mass( 40g*13) must b equal to the distance from the pivot to the center of mass* mass(10*xg).
Doing the simple calculation,the answer has to be 52g

the center of mass of the rule is at the 25 cm mark

40 g * (15 cm - 2 cm) = M * (25 cm - 15 cm)

Auniform half meter rule is pivoted at 15cm mark and balanced horizontally when a body of mass 40g is hanging from the 2cm mark.calculate the mass of the half meter rule

To solve this problem, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.

In this case, the rule is balanced horizontally, so the sum of the clockwise moments is equal to the sum of the anticlockwise moments. Let's calculate the moments on each side separately.

Clockwise moments:
The mass of the rule can be assumed to be concentrated at its center of gravity, which is at the mid-point of the rule. So the distance from the pivot to the center of gravity is 0.5/2 = 0.25 cm. The clockwise moment is then given by the mass of the rule multiplied by the distance from the pivot:

Clockwise moment = mass of the rule * distance from pivot
= mass of the rule * 0.25 cm

Anticlockwise moments:
The body of mass 40g is hung from the 2cm mark. The distance from the pivot to this point is 15cm - 2cm = 13cm. The anticlockwise moment is given by the mass of the body multiplied by the distance from the pivot:

Anticlockwise moment = mass of the body * distance from pivot
= 40g * 13cm

Since the sum of the clockwise moments is equal to the sum of the anticlockwise moments, we can set up the equation:

mass of the rule * 0.25 cm = 40g * 13cm

To solve for the mass of the rule, divide both sides of the equation by 0.25 cm:

mass of the rule = (40g * 13cm) / 0.25 cm

mass of the rule ≈ 2080g

Therefore, the mass of the rule is approximately 2080 grams.

I dnt know

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