gyration of disc:
The radius of gyration of a disc can be calculated using the formula:
k = R/√2
where k is the radius of gyration, R is the radius of the disc, and √2 is a constant.
In this case, the mass of the disc is 100 grams and the radius is 5 cm. The first step is to convert the mass to kilograms, which gives:
m = 0.1 kg
The moment of inertia of the disc about an axis passing through its centre of gravity and perpendicular to its plane is given by:
I = (1/2)mr^2
where r is the radius of the disc. Substituting the values given, we get:
I = (1/2)(0.1 kg)(0.05 m)^2 = 1.25 × 10^-4 kg m^2
The radius of gyration can then be calculated using the formula above:
k = R/√2 = (0.05 m)/√2 = 0.0354 m
Therefore, the radius of gyration of the disc is approximately 0.0354 meters.