In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is $$l$$ = 25 cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing distance $$l'$$ (in cm) will now be________.

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

For the four sets of three measured physical quantities as given below. Which of the following options is correct ?
(i) A₁ = 24.36, B₁ = 0.0724, C₁ = 256.2
(ii) A₂ = 24.44, B₂ = 16.082, C₂ = 240.2
(iii) A₃ = 25.2, B₃ = 19.2812, C₃ = 236.183
(iv) A₄ = 25, B₄ = 236.191, C₄ = 19.5

Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are v_A and v_B, respectively, then $${{{v_A}} \over {{v_B}}} = {n \over 4}$$. The value of n is :