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 :

A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho $$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :

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

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then :