Answer :
The balancing weight needed is 20g
What is center of gravity?
The center of gravity is the average position of the weight of an object. We can fully describe the movement of an object through space in terms of the displacement of the object's center of mass from one place to another and the rotation of the object around its center of mass if it is free to rotate.
Given,
Given radius of wheel rim (R): 20 cm
Center of gravity 1 mm away from axis of rotation (z-axis)
This indicates imbalance on x-y plane,
Now, let's assume unbalanced weight is more towards positive x-axis, hence the center of gravity is towards positive x-direction.
In order to statically balance the mass and bring center of gravity towards z-axis, we need to place similar amount of mass 1 mm in negative x-direction.
But as we know adding huge weight to wheel is always unpreferable so we will add M amount of weight on -20 cm in x-direction.
In order to balance the weight, moment about the central axis should be zero.
∑M₀ = 0
10000g × 1 mm = M × 200 mm
M = 10000/200
M = 20g
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