Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 10³ kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 10¹¹ Pa, g = 9.8 m/s²]

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)