A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 80 GPa. While operating at 500 rpm, the angle of twist across its length is found to be 0.5 degrees.

The power transmitted by the shaft at this speed is _______kW. (Rounded off to two decimal places)

Take π = 3.14.

A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for positioning. Four different configurations of locating pins are proposed as shown. Which one of the options given is correct?

Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio |ω2 |/|ω1 | = 1/4, have their centers 30 mm apart. The number of teeth on the driver (gear 1) is _______ .

(Answer in integer)

The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant k = 1000 N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is _________ seconds. (Rounded off to two decimal places)

Take π = 3.14.