Asteel sphere with radius 1.0010 cm at 41.0°c must slip through a brass ring that has an internal radius of 1. cm at the same temperature. to what temperature must the brass ring be heated so that the sphere, still at 41.0°c, can just slip through? coefficient of linear expansion α for brass is 19.0 × 10−6 k−1.

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)