A uniform heavy rod of weight 10 kg ms^$$-$$2, cross-sectional area 100 cm² and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $$\times$$ 10¹¹ Nm^$$-$$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10^$$-$$5 m and density 1.2 $$\times$$ 10³ kgm^$$-$$3 ? Take viscosity of liquid = 1.8 $$\times$$ 10^$$-$$5 Nsm^$$-$$2. (Neglect buoyancy due to air).

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $${{24} \over \pi } \times {10^2}$$ Nm^-2. What is the minimum radius of the wire ? (Take g = 10 ms^-2)

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $$\times$$ 10^$$-$$2 Nm^$$-$$1, angle of contact = 0, g = 10 ms² and density of water = 1.0 $$\times$$ 10³ kg m^$$-$$3]