A uniform stick Ab can be balanced on a knife edge 10cm from one end when a weight of 200N is hung from that end the 200N weight has to be moved to a point 8.75cm from the knife edge to obtain a balance .Find the length of the stick and its weight
To find the length of the stick and its weight, 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 about any point must be equal to the sum of the anticlockwise moments about the same point.
Let's consider the balance point at the knife edge and take moments about it.
When the weight of 200N is hung 10cm from one end of the stick, we have the following moments:
Clockwise moment = 200N x 10cm = 2000Ncm
Now, when the 200N weight is moved to a point 8.75cm from the knife edge, the stick will be balanced. So, the anticlockwise moment created by this weight is equal to the clockwise moment created by the weight of the stick itself.
Let's assume the length of the stick is 'x' cm. Therefore, the distance of the weight from the knife edge will be (x - 8.75) cm.
So, the moments created by the weight of the stick itself are:
Anticlockwise moment = Weight of the stick x (x - 8.75) cm
Since the stick is uniform, its weight can be considered to act at its center. Therefore, the weight of the stick will be half the total weight of 200N, which is 100N.
Now, to obtain a balance, the clockwise moment and the anticlockwise moment must be equal. Therefore:
2000Ncm = 100N x (x - 8.75) cm
Simplifying the equation:
2000 = 100(x - 8.75)
2000 = 100x - 875
100x = 2875
x = 28.75 cm
So, the length of the stick is 28.75 cm.
To find the weight of the stick itself, we know that it is half the total weight of 200N, which is 100N.
Therefore, the weight of the stick is 100N.
Hence, the length of the stick is 28.75 cm, and its weight is 100N.