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.

Two plane mirrors M₁ and M₂ are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M₁ and M₂ respectively. The shortest distance between the images thus formed is : (Take $$\sqrt 5 $$ = 2.3)

Match List - I with List - II.

	List - I		List - II
(a)	Torque	(i)	MLT$$^{ - 1}$$
(b)	Impulse	(ii)	MT$$^{ - 2}$$
(c)	Tension	(iii)	ML$$^{ 2}$$T$$^{ - 2}$$
(d)	Surface Tension	(iv)	MLT$$^{ - 2}$$

Choose the most appropriate answer from the option given below :

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $${{dp} \over {dv}} = - ap$$. If p = p₀ at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)