A circular specimen of MgO is loaded using a three-point bending mode. Compute the minimum possible radius of the specimen without fracture, given that the applied load is 1500 N (337 lbf), the flexural strength is 105 MPa (15,000 psi), and the separation between load points is 50.0 mm (1.97 in.)

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?