A free bar of length 1 m is uniformly heated from $${0^ \circ }C$$ to a temperature of $${t^ \circ }C$$. $$\alpha $$ is the coefficient if linear expansion and $$E$$ the modulus of elasticity. The stress in the bar is

Fig. shows a quick return mechanism. The crank $$OA$$ rotates clockwise uniformly. $$OA=2$$ cm, $$O{O^1} = 4$$ cm. The ratio of time for forward motion to that for return motion is

List $$I$$ (Gear types)
(a) Worm gears
(b) Cross helical gears
(c) Bevel gears
(d) Spur gears

List $$II$$ (Applications)
1. Parallel shafts
2. Non-parallel, intersecting shafts
3. Non-parallel, non intersecting shafts
4. Large speed ratios

The arm OA of an epicylic gear train shown in Fig. revolves counter clockwise about O with an angular velocity of 4 rad/sec. Both gears are of same size. The angular velocity of gear C, if the sun gear B is fixed, is