A weight of 1000 grams hangs from a lever 20cm to the fulcrum. At the left is a 500-gram weight 20cm from the fulcrum, and a 200-gram weight x cm away from the fulcrum. What is the value of x that will make the lever balanced?
50cm
20cm
10cm
30cm
70cm
Explanation
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m1 = 1000g = 1kg
m2 = 500g = 0.5kg
m3 = 200g = 0.2kg
Clockwise moment
= 0.2x (10) + 0.5 × 20 × 10
= 2x + 100
Anticlockwise moment
= 1 × 20 × 10
= 200
By the principle of moments:
2x + 100 = 200
2x = 200 - 100
2x = 100
x = 50cm
🤍
My school please correct this, both your answer and explanation is wrong. you got me thinking what I did wrong.
The question said 200g away from the Fulcrum and not away from the 300g
so it's
(200 × X) + (300 × 20) =( 500 × 20)
solve and get 50cm
no need adding 20 to x, that's only necessary when it's away from the 300g and not the fulcrum.
• On the right side of the lever:
A weight of 1000 grams is placed 20 cm from the fulcrum.
• On the left side of the lever:A weight of 500 grams is placed 20 cm from the fulcrum.
A weight of 200 grams is placed x cm from the fulcrum.
We are asked to find the value of x that will make the lever balanced.
Step 1:. For the lever to be balanced, the sum of the moments on the left side must equal the sum of the moments on the right side.
1. Left side( anticlockwise moment)Note There are two weights on the left side:
The moment due to the 500-gram weight:
• Moment = 500 × 20 = 10,000gram-cm
• The moment due to the 200-gram weight at x cm:
So, the total moment on the left side is: Total moment on left=(10,000+200x)
2. Right hand (clockwise moment): There is only one weight on the right side:
The moment due to the 1000-gram weight:
Moment=1000×20= 20,000gram
Step2: Set up a balance equation I.e Anticlockwise moment = Clockwise moment 10,000 + 200x = 20,000
Step3: solve for x 200x = 20,000 – 10,000
200x = 10,000
:. x = 10,000/200
x = 50cm
clock wise or right side or whatever: 1000 * 20 = 20000
left: 500 * 20 + 200 * x = 10000 + 200x
for lever's equilibrium:
left side = right side
10000 + 200x = 20000
200x = 10000
x = 50 👌
Due to the fact that the question was away from the fulcrum and not from the 20cm mark .
To solve this lever balance problem, we use the principle of moments, which states:
Sum of clockwise moments = Sum of anticlockwise moments (for balance).
Given:
A 1000g weight hangs from a lever 20 cm to the right of the fulcrum.
A 500g weight is 20 cm to the left.
A 200g weight is x cm to the left.
We need to find x so the lever is balanced.
Step-by-step:
Clockwise moment (right side):
Anticlockwise moments (left side):
So for balance:
10000 + 200x = 20000
Solving for :
200x = 10000 \Rightarrow x = \frac{10000}{200} = 50
Final Answer: A. 50 cm
