Aten-centimeter radius thorium sphere with a thermal conductivity of 55 w/mk experiences a uniform heat generation rate of 1x106 w/m. the sphere is surrounded by air at 20°c with a film coefficient of 500 w/m-k. determine the total heat transfer from the sphere to the air and the temperatures at the following locations: (1) the sphere center; (2) at a radius of 5 cm; and (3) at the sphere surface.

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed