An iron circular disc is rotated about its axis with a constant angular velocity . Determine the percentage change in the linear speed of a particle on the rim when the disc is gradually heated from 20^ C to 50^ C while maintaining the angular velocity constant. The coefficient of linear expansion of iron is 1.2 10⁻⁵ ^ C⁻¹ .

Step-by-step solution

The linear speed of a particle on the rim of the disc is given by v = R , where R is the radius and is the angular velocity. Since the angular velocity is maintained constant, the fractional change in the linear speed is equal to the fractional change in the radius. v v = R R Due to thermal expansion, the change in radius is given by R = R T , which implies R R = T . Therefore, the percentage change in linear speed is: v v 100 = T 100 Substituting the given values, = 1.2 10⁻⁵ ^ C ⁻¹ and T = 50^ C - 20^ C = 30^ C :