Three liquids of densities 1, 2 and 3 (with 1 > 2 > 3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ1, θ2 and θ3 obey

A rectangular film of liquid is extended from (4 cm × 2cm) to (5 cm × 4 cm). If the work done is 3 × 10^–4 J, the value of the surface tension of the liquid is

A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g0, the value of acceleration due to gravity at the earth's surface, is

Starting from the centre of the earth having radius r, the variation of g (acceleration due to gravity) is shown by

A light rod of length l has two masses m₁ and mattached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is :

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (E_sphere / E cylinder) will be :