a uniform stick can be balanced on a knife edge 10cm from one end when a load of 200N is hung from that end . when the knife edgeis moved 5cm further from the end the 200N load has to be moved to a point 8.75cm from the knife edge to obtain balance . find the length of the stick and its weight
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To find the length of the stick, we can use the principle of moments.
Let's assume the length of the stick is 'L'.
In the first scenario, when the knife edge is 10cm from one end and the load of 200N is hung from that end, we can set up the equation:
200N * 10cm = W * (L - 10cm)
where W represents the weight of the stick.
In the second scenario, when the knife edge is moved 5cm further from the end and the 200N load is moved to a point 8.75cm from the knife edge, we can set up the equation:
200N * 15cm = W * (L - 15cm - 8.75cm)
By multiplying both sides of the equations by 10 and 15 respectively, we get:
2000N * cm = 10W * cm
3000N * cm = 15W * cm
Simplifying the equations, we have:
2000N = 10W
3000N = 15W
Dividing the second equation by 3 and the first equation by 2, we get:
1000N = 5W
1000N = 10W
From these two equations, we can conclude that 5W = 10W, which implies W equals zero.
Therefore, the weight of the stick is 0N, which means it is weightless.
Now, substituting the value of W in the first equation, we have:
2000N = 10 * 0
2000N = 0
This equation is true for all values of N, which means the length of the stick could be any real number.
In conclusion, the length of the stick can be any real number and its weight is 0N, indicating that it is weightless.
To solve this problem, we can use the principle of moments. The principle of moments states that for a body in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
Let's assign variables to the unknowns:
Length of the stick = L
Weight of the stick = W
First, let's consider the initial situation where the knife edge is 10 cm from one end and the load of 200 N is hung from that end. The stick is balanced in this position.
The clockwise moment about the knife edge is the product of the load (200 N) and the distance from the knife edge (10 cm). So, the clockwise moment is 200 N * 10 cm.
Now, let's consider the second situation where the knife edge is moved 5 cm further from the end, and the load of 200 N is moved to a point 8.75 cm from the knife edge to balance the stick.
The anticlockwise moment about the knife edge can be calculated as the product of the load (200 N) and the distance from the knife edge (8.75 cm). So, the anticlockwise moment is 200 N * 8.75 cm.
According to the principle of moments, the clockwise moment in the initial situation is equal to the anticlockwise moment in the second situation. Therefore:
200 N * 10 cm = 200 N * 8.75 cm
Now, let's solve for L, the length of the stick:
200 N * 10 cm = 200 N * 8.75 cm
2000 N cm = 1750 N cm
2000 N cm / 1750 N cm = L
L = 1.14 m
Finally, let's find the weight of the stick, W:
The weight of the stick is equal to the load in both cases. Therefore, W = 200 N.
So, the length of the stick is 1.14 m and the weight of the stick is 200 N.