Two spheres P and Q for equal radii have densities $$\rho$$₁ and $$\rho$$₂, respectively. The spheres are connected by a massless string and placed in liquids L₁ and L₂ of densities $$\sigma$$₁ and $$\sigma$$₂ and viscosities $${\eta _1}$$ and $${\eta _2}$$, respectively. They float in equilibrium with the sphere P in L₁ and sphere Q in L₂ and the string being taut (see figure) If sphere P along in L₂ has terminal velocity v_P and Q alone in L₁ ha terminal velocity v_Q, then

Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n₁ surrounded by a medium of lower refractive index n₂. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n₁ and n₂ as shown in the figure. All rays with the angle of incidence i less than a particular value i_m are confined in the medium of refractive index n₁. The numerical aperture (NA) of the structure is defined as sin i_m.

For two structures namely S₁ with n₁ = $${{\sqrt {45} } \over 4}$$ and n₂ = $${3 \over 2}$$, and S₂ with n₁ = $${8 \over 5}$$ and n₂ = $${7 \over 5}$$ and taking the refractive index of water to be $${4 \over 3}$$ and that to air to be 1, the correct options is/are :

Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n₁ surrounded by a medium of lower refractive index n₂. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n₁ and n₂ as shown in the figure. All rays with the angle of incidence i less than a particular value i_m are confined in the medium of refractive index n₁. The numerical aperture (NA) of the structure is defined as sin i_m.

If two structures of same cross-sectional area, but different numeral apertures NA₁ and NA₂ (NA₂ < NA₁) are joined longitudinally, the numerical aperture of the combined structure is

In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively.

A uniform magnetic field B is applied on the strip along the positive y-direction. Due to this, the charge carriers experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w₁ and w₂ and thickness are d₁ and d₂, respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V₁ and V₂ are the potential differences between K and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statements is/are